TY - GEN
AB - We consider the core algorithmic problems related to verification of systems with respect to three classical quantitative properties, namely, the mean-payoff property, the ratio property, and the minimum initial credit for energy property.
The algorithmic problem given a graph and a quantitative property asks to compute the optimal value (the infimum value over all traces) from every node of the graph. We consider graphs with constant treewidth, and it is well-known that the control-flow graphs of most programs have constant treewidth. Let $n$ denote the number of nodes of a graph, $m$ the number of edges (for constant treewidth graphs $m=O(n)$) and $W$ the largest absolute value of the weights.
Our main theoretical results are as follows.
First, for constant treewidth graphs we present an algorithm that approximates the mean-payoff value within a multiplicative factor of $\epsilon$ in time $O(n \cdot \log (n/\epsilon))$ and linear space, as compared to the classical algorithms that require quadratic time. Second, for the ratio property we present an algorithm that for constant treewidth graphs works in time $O(n \cdot \log (|a\cdot b|))=O(n\cdot\log (n\cdot W))$, when the output is $\frac{a}{b}$, as compared to the previously best known algorithm with running time $O(n^2 \cdot \log (n\cdot W))$. Third, for the minimum initial credit problem we show that (i)~for general graphs the problem can be solved in $O(n^2\cdot m)$ time and the associated decision problem can be solved in $O(n\cdot m)$ time, improving the previous known $O(n^3\cdot m\cdot \log (n\cdot W))$ and $O(n^2 \cdot m)$ bounds, respectively; and (ii)~for constant treewidth graphs we present an algorithm that requires $O(n\cdot \log n)$ time, improving the previous known $O(n^4 \cdot \log (n \cdot W))$ bound.
We have implemented some of our algorithms and show that they present a significant speedup on standard benchmarks.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Pavlogiannis, Andreas
ID - 5437
SN - 2664-1690
TI - Faster algorithms for quantitative verification in constant treewidth graphs
ER -
TY - GEN
AB - The edit distance between two words w1, w2 is the minimal number of word operations (letter insertions, deletions, and substitutions) necessary to transform w1 to w2. The edit distance generalizes to languages L1, L2, where the edit distance is the minimal number k such that for every word from L1 there exists a word in L2 with edit distance at most k. We study the edit distance computation problem between pushdown automata and their subclasses.
The problem of computing edit distance to a pushdown automaton is undecidable, and in practice, the interesting question is to compute the edit distance from a pushdown automaton (the implementation, a standard model for programs with recursion) to a regular language (the specification). In this work, we present a complete picture of decidability and complexity for deciding whether, for a given threshold k, the edit distance from a pushdown automaton to a finite automaton is at most k.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Ibsen-Jensen, Rasmus
AU - Otop, Jan
ID - 5438
SN - 2664-1690
TI - Edit distance for pushdown automata
ER -
TY - GEN
AB - The target discounted-sum problem is the following: Given a rational discount factor 0 < λ < 1 and three rational values a, b, and t, does there exist a finite or an infinite sequence w ε(a, b)∗ or w ε(a, b)w, such that Σ|w| i=0 w(i)λi equals t? The problem turns out to relate to many fields of mathematics and computer science, and its decidability question is surprisingly hard to solve. We solve the finite version of the problem, and show the hardness of the infinite version, linking it to various areas and open problems in mathematics and computer science: β-expansions, discounted-sum automata, piecewise affine maps, and generalizations of the Cantor set. We provide some partial results to the infinite version, among which are solutions to its restriction to eventually-periodic sequences and to the cases that λ λ 1/2 or λ = 1/n, for every n ε N. We use our results for solving some open problems on discounted-sum automata, among which are the exact-value problem for nondeterministic automata over finite words and the universality and inclusion problems for functional automata.
AU - Boker, Udi
AU - Henzinger, Thomas A
AU - Otop, Jan
ID - 5439
SN - 2664-1690
TI - The target discounted-sum problem
ER -
TY - GEN
AB - Evolution occurs in populations of reproducing individuals. The structure of the population affects the outcome of the evolutionary process. Evolutionary graph theory is a powerful approach to study this phenomenon. There are two graphs. The interaction graph specifies who interacts with whom for payoff in the context of evolution. The replacement graph specifies who competes with whom for reproduction. The vertices of the two graphs are the same, and each vertex corresponds to an individual of the population. The fitness (or the reproductive rate) is a non-negative number, and depends on the payoff. A key quantity is the fixation probability of a new mutant. It is defined as the probability that a newly introduced mutant (on a single vertex) generates a lineage of offspring which eventually takes over the entire population of resident individuals. The basic computational questions are as follows: (i) the qualitative question asks whether the fixation probability is positive; and (ii) the quantitative approximation question asks for an approximation of the fixation probability. Our main results are as follows: First, we consider a special case of the general problem, where the residents do not reproduce. We show that the qualitative question is NP-complete, and the quantitative approximation question is #P-complete, and the hardness results hold even in the special case where the interaction and the replacement graphs coincide. Second, we show that in general both the qualitative and the quantitative approximation questions are PSPACE-complete. The PSPACE-hardness result for quantitative approximation holds even when the fitness is always positive.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Nowak, Martin
ID - 5440
SN - 2664-1690
TI - The complexity of evolutionary games on graphs
ER -
TY - GEN
AB - We study algorithmic questions for concurrent systems where the transitions are labeled from a complete, closed semiring, and path properties are algebraic with semiring operations. The algebraic path properties can model dataflow analysis problems, the shortest path problem, and many other natural problems that arise in program analysis. We consider that each component of the concurrent system is a graph with constant treewidth, a property satisfied by the controlflow graphs of most programs. We allow for multiple possible queries, which arise naturally in demand driven dataflow analysis. The study of multiple queries allows us to consider the tradeoff between the resource usage of the one-time preprocessing and for each individual query. The traditional approach constructs the product graph of all components and applies the best-known graph algorithm on the product. In this approach, even the answer to a single query requires the transitive closure (i.e., the results of all possible queries), which provides no room for tradeoff between preprocessing and query time. Our main contributions are algorithms that significantly improve the worst-case running time of the traditional approach, and provide various tradeoffs depending on the number of queries. For example, in a concurrent system of two components, the traditional approach requires hexic time in the worst case for answering one query as well as computing the transitive closure, whereas we show that with one-time preprocessing in almost cubic time, each subsequent query can be answered in at most linear time, and even the transitive closure can be computed in almost quartic time. Furthermore, we establish conditional optimality results showing that the worst-case running time of our algorithms cannot be improved without achieving major breakthroughs in graph algorithms (i.e., improving the worst-case bound for the shortest path problem in general graphs). Preliminary experimental results show that our algorithms perform favorably on several benchmarks.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Goharshady, Amir
AU - Pavlogiannis, Andreas
ID - 5441
SN - 2664-1690
TI - Algorithms for algebraic path properties in concurrent systems of constant treewidth components
ER -
TY - GEN
AB - We study algorithmic questions for concurrent systems where the transitions are labeled from a complete, closed semiring, and path properties are algebraic with semiring operations. The algebraic path properties can model dataflow analysis problems, the shortest path problem, and many other natural properties that arise in program analysis.
We consider that each component of the concurrent system is a graph with constant treewidth, and it is known that the controlflow graphs of most programs have constant treewidth. We allow for multiple possible queries, which arise naturally in demand driven dataflow analysis problems (e.g., alias analysis). The study of multiple queries allows us to consider the tradeoff between the resource usage of the \emph{one-time} preprocessing and for \emph{each individual} query. The traditional approaches construct the product graph of all components and apply the best-known graph algorithm on the product. In the traditional approach, even the answer to a single query requires the transitive closure computation (i.e., the results of all possible queries), which provides no room for tradeoff between preprocessing and query time.
Our main contributions are algorithms that significantly improve the worst-case running time of the traditional approach, and provide various tradeoffs depending on the number of queries. For example, in a concurrent system of two components, the traditional approach requires hexic time in the worst case for answering one query as well as computing the transitive closure, whereas we show that with one-time preprocessing in almost cubic time,
each subsequent query can be answered in at most linear time, and even the transitive closure can be computed in almost quartic time. Furthermore, we establish conditional optimality results that show that the worst-case running times of our algorithms cannot be improved without achieving major breakthroughs in graph algorithms (such as improving
the worst-case bounds for the shortest path problem in general graphs whose current best-known bound has not been improved in five decades). Finally, we provide a prototype implementation of our algorithms which significantly outperforms the existing algorithmic methods on several benchmarks.
AU - Anonymous, 1
AU - Anonymous, 2
AU - Anonymous, 3
AU - Anonymous, 4
ID - 5442
SN - 2664-1690
TI - Algorithms for algebraic path properties in concurrent systems of constant treewidth components
ER -
TY - GEN
AB - POMDPs are standard models for probabilistic planning problems, where an agent interacts with an uncertain environment. We study the problem of almost-sure reachability, where given a set of target states, the question is to decide whether there is a policy to ensure that the target set is reached with probability 1 (almost-surely). While in general the problem is EXPTIME-complete, in many practical cases policies with a small amount of memory suffice. Moreover, the existing solution to the problem is explicit, which first requires to construct explicitly an exponential reduction to a belief-support MDP. In this work, we first study the existence of observation-stationary strategies, which is NP-complete, and then small-memory strategies. We present a symbolic algorithm by an efficient encoding to SAT and using a SAT solver for the problem. We report experimental results demonstrating the scalability of our symbolic (SAT-based) approach.
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Davies, Jessica
ID - 5443
SN - 2664-1690
TI - A symbolic SAT-based algorithm for almost-sure reachability with small strategies in POMDPs
ER -
TY - GEN
AB - A comprehensive understanding of the clonal evolution of cancer is critical for understanding neoplasia. Genome-wide sequencing data enables evolutionary studies at unprecedented depth. However, classical phylogenetic methods often struggle with noisy sequencing data of impure DNA samples and fail to detect subclones that have different evolutionary trajectories. We have developed a tool, called Treeomics, that allows us to reconstruct the phylogeny of a cancer with commonly available sequencing technologies. Using Bayesian inference and Integer Linear Programming, robust phylogenies consistent with the biological processes underlying cancer evolution were obtained for pancreatic, ovarian, and prostate cancers. Furthermore, Treeomics correctly identified sequencing artifacts such as those resulting from low statistical power; nearly 7% of variants were misclassified by conventional statistical methods. These artifacts can skew phylogenies by creating illusory tumor heterogeneity among distinct samples. Importantly, we show that the evolutionary trees generated with Treeomics are mathematically optimal.
AU - Reiter, Johannes
AU - Makohon-Moore, Alvin
AU - Gerold, Jeffrey
AU - Bozic, Ivana
AU - Chatterjee, Krishnendu
AU - Iacobuzio-Donahue, Christine
AU - Vogelstein, Bert
AU - Nowak, Martin
ID - 5444
SN - 2664-1690
TI - Reconstructing robust phylogenies of metastatic cancers
ER -
TY - GEN
AB - Model-based testing is a promising technology for black-box software and hardware testing, in which test cases are generated automatically from high-level specifications. Nowadays, systems typically consist of multiple interacting components and, due to their complexity, testing presents a considerable portion of the effort and cost in the design process. Exploiting the compositional structure of system specifications can considerably reduce the effort in model-based testing. Moreover, inferring properties about the system from testing its individual components allows the designer to reduce the amount of integration testing.
In this paper, we study compositional properties of the IOCO-testing theory. We propose a new approach to composition and hiding operations, inspired by contract-based design and interface theories. These operations preserve behaviors that are compatible under composition and hiding, and prune away incompatible ones. The resulting specification characterizes the input sequences for which the unit testing of components is sufficient to infer the correctness of component integration without the need for further tests. We provide a methodology that uses these results to minimize integration testing effort, but also to detect potential weaknesses in specifications. While we focus on asynchronous models and the IOCO conformance relation, the resulting methodology can be applied to a broader class of systems.
AU - Daca, Przemyslaw
AU - Henzinger, Thomas A
AU - Krenn, Willibald
AU - Nickovic, Dejan
ID - 5411
SN - 2664-1690
TI - Compositional specifications for IOCO testing
ER -
TY - GEN
AB - We consider Markov decision processes (MDPs) which are a standard model for probabilistic systems. We focus on qualitative properties for MDPs that can express that desired behaviors of the system arise almost-surely (with probability 1) or with positive probability.
We introduce a new simulation relation to capture the refinement relation of MDPs with respect to qualitative properties, and present discrete graph theoretic algorithms with quadratic complexity to compute the simulation relation.
We present an automated technique for assume-guarantee style reasoning for compositional analysis of MDPs with qualitative properties by giving a counter-example guided abstraction-refinement approach to compute our new simulation relation. We have implemented our algorithms and show that the compositional analysis leads to significant improvements.
AU - Chatterjee, Krishnendu
AU - Daca, Przemyslaw
AU - Chmelik, Martin
ID - 5412
SN - 2664-1690
TI - CEGAR for qualitative analysis of probabilistic systems
ER -
TY - GEN
AB - We consider Markov decision processes (MDPs) which are a standard model for probabilistic systems. We focus on qualitative properties for MDPs that can express that desired behaviors of the system arise almost-surely (with probability 1) or with positive probability.
We introduce a new simulation relation to capture the refinement relation of MDPs with respect to qualitative properties, and present discrete graph theoretic algorithms with quadratic complexity to compute the simulation relation.
We present an automated technique for assume-guarantee style reasoning for compositional analysis of MDPs with qualitative properties by giving a counter-example guided abstraction-refinement approach to compute our new simulation relation. We have implemented our algorithms and show that the compositional analysis leads to significant improvements.
AU - Chatterjee, Krishnendu
AU - Daca, Przemyslaw
AU - Chmelik, Martin
ID - 5413
SN - 2664-1690
TI - CEGAR for qualitative analysis of probabilistic systems
ER -
TY - GEN
AB - We consider Markov decision processes (MDPs) which are a standard model for probabilistic systems. We focus on qualitative properties for MDPs that can express that desired behaviors of the system arise almost-surely (with probability 1) or with positive probability.
We introduce a new simulation relation to capture the refinement relation of MDPs with respect to qualitative properties, and present discrete graph theoretic algorithms with quadratic complexity to compute the simulation relation.
We present an automated technique for assume-guarantee style reasoning for compositional analysis of MDPs with qualitative properties by giving a counter-example guided abstraction-refinement approach to compute our new simulation relation.
We have implemented our algorithms and show that the compositional analysis leads to significant improvements.
AU - Chatterjee, Krishnendu
AU - Daca, Przemyslaw
AU - Chmelik, Martin
ID - 5414
SN - 2664-1690
TI - CEGAR for qualitative analysis of probabilistic systems
ER -
TY - GEN
AB - Recently there has been a significant effort to add quantitative properties in formal verification and synthesis. While weighted automata over finite and infinite words provide a natural and flexible framework to express quantitative properties, perhaps surprisingly, several basic system properties such as average response time cannot be expressed with weighted automata. In this work, we introduce nested weighted automata as a new formalism for expressing important quantitative properties such as average response time. We establish an almost complete decidability picture for the basic decision problems for nested weighted automata, and illustrate its applicability in several domains.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Otop, Jan
ID - 5415
SN - 2664-1690
TI - Nested weighted automata
ER -
TY - GEN
AB - As hybrid systems involve continuous behaviors, they should be evaluated by quantitative methods, rather than qualitative methods. In this paper we adapt a quantitative framework, called model measuring, to the hybrid systems domain. The model-measuring problem asks, given a model M and a specification, what is the maximal distance such that all models within that distance from M satisfy (or violate) the specification. A distance function on models is given as part of the input of the problem. Distances, especially related to continuous behaviors are more natural in the hybrid case than the discrete case. We are interested in distances represented by monotonic hybrid automata, a hybrid counterpart of (discrete) weighted automata, whose recognized timed languages are monotone (w.r.t. inclusion) in the values of parameters.The contributions of this paper are twofold. First, we give sufficient conditions under which the model-measuring problem can be solved. Second, we discuss the modeling of distances and applications of the model-measuring problem.
AU - Henzinger, Thomas A
AU - Otop, Jan
ID - 5416
SN - 2664-1690
TI - Model measuring for hybrid systems
ER -
TY - GEN
AB - We define the model-measuring problem: given a model M and specification φ, what is the maximal distance ρ such that all models M'within distance ρ from M satisfy (or violate)φ. The model measuring problem presupposes a distance function on models. We concentrate on automatic distance functions, which are defined by weighted automata.
The model-measuring problem subsumes several generalizations of the classical model-checking problem, in particular, quantitative model-checking problems that measure the degree of satisfaction of a specification, and robustness problems that measure how much a model can be perturbed without violating the specification.
We show that for automatic distance functions, and ω-regular linear-time and branching-time specifications, the model-measuring problem can be solved.
We use automata-theoretic model-checking methods for model measuring, replacing the emptiness question for standard word and tree automata by the optimal-weight question for the weighted versions of these automata. We consider weighted automata that accumulate weights by maximizing, summing, discounting, and limit averaging.
We give several examples of using the model-measuring problem to compute various notions of robustness and quantitative satisfaction for temporal specifications.
AU - Henzinger, Thomas A
AU - Otop, Jan
ID - 5417
SN - 2664-1690
TI - From model checking to model measuring
ER -
TY - GEN
AB - We consider multi-player graph games with partial-observation and parity objective. While the decision problem for three-player games with a coalition of the first and second players against the third player is undecidable, we present a decidability result for partial-observation games where the first and third player are in a coalition against the second player, thus where the second player is adversarial but weaker due to partial-observation. We establish tight complexity bounds in the case where player 1 is less informed than player 2, namely 2-EXPTIME-completeness for parity objectives. The symmetric case of player 1 more informed than player 2 is much more complicated, and we show that already in the case where player 1 has perfect observation, memory of size non-elementary is necessary in general for reachability objectives, and the problem is decidable for safety and reachability objectives. Our results have tight connections with partial-observation stochastic games for which we derive new complexity results.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
ID - 5418
SN - 2664-1690
TI - Games with a weak adversary
ER -
TY - GEN
AB - We consider the reachability and shortest path problems on low tree-width graphs, with n nodes, m edges, and tree-width t, on a standard RAM with wordsize W. We use O to hide polynomial factors of the inverse of the Ackermann function. Our main contributions are three fold:
1. For reachability, we present an algorithm that requires O(n·t2·log(n/t)) preprocessing time, O(n·(t·log(n/t))/W) space, and O(t/W) time for pair queries and O((n·t)/W) time for single-source queries. Note that for constant t our algorithm uses O(n·logn) time for preprocessing; and O(n/W) time for single-source queries, which is faster than depth first search/breath first search (after the preprocessing).
2. We present an algorithm for shortest path that requires O(n·t2) preprocessing time, O(n·t) space, and O(t2) time for pair queries and O(n·t) time single-source queries.
3. We give a space versus query time trade-off algorithm for shortest path that, given any constant >0, requires O(n·t2) preprocessing time, O(n·t2) space, and O(n1−·t2) time for pair queries.
Our algorithms improve all existing results, and use very simple data structures.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Pavlogiannis, Andreas
ID - 5419
SN - 2664-1690
TI - Improved algorithms for reachability and shortest path on low tree-width graphs
ER -
TY - GEN
AB - We consider concurrent mean-payoff games, a very well-studied class of two-player (player 1 vs player 2) zero-sum games on finite-state graphs where every transition is assigned a reward between 0 and 1, and the payoff function is the long-run average of the rewards. The value is the maximal expected payoff that player 1 can guarantee against all strategies of player 2. We consider the computation of the set of states with value 1 under finite-memory strategies for player 1, and our main results for the problem are as follows: (1) we present a polynomial-time algorithm; (2) we show that whenever there is a finite-memory strategy, there is a stationary strategy that does not need memory at all; and (3) we present an optimal bound (which is double exponential) on the patience of stationary strategies (where patience of a distribution is the inverse of the smallest positive probability and represents a complexity measure of a stationary strategy).
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
ID - 5420
SN - 2664-1690
TI - The value 1 problem for concurrent mean-payoff games
ER -
TY - GEN
AB - Evolution occurs in populations of reproducing individuals. The structure of the population affects the outcome of the evolutionary process. Evolutionary graph theory is a powerful approach to study this phenomenon. There are two graphs. The interaction graph specifies who interacts with whom in the context of evolution. The replacement graph specifies who competes with whom for reproduction. The vertices of the two graphs are the same, and each vertex corresponds to an individual. A key quantity is the fixation probability of a new mutant. It is defined as the probability that a newly introduced mutant (on a single vertex) generates a lineage of offspring which eventually takes over the entire population of resident individuals. The basic computational questions are as follows: (i) the qualitative question asks whether the fixation probability is positive; and (ii) the quantitative approximation question asks for an approximation of the fixation probability. Our main results are: (1) We show that the qualitative question is NP-complete and the quantitative approximation question is #P-hard in the special case when the interaction and the replacement graphs coincide and even with the restriction that the resident individuals do not reproduce (which corresponds to an invading population taking over an empty structure). (2) We show that in general the qualitative question is PSPACE-complete and the quantitative approximation question is PSPACE-hard and can be solved in exponential time.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Nowak, Martin
ID - 5421
SN - 2664-1690
TI - The complexity of evolution on graphs
ER -
TY - GEN
AB - We present a flexible framework for the automated competitive analysis of on-line scheduling algorithms for firm- deadline real-time tasks based on multi-objective graphs: Given a taskset and an on-line scheduling algorithm specified as a labeled transition system, along with some optional safety, liveness, and/or limit-average constraints for the adversary, we automatically compute the competitive ratio of the algorithm w.r.t. a clairvoyant scheduler. We demonstrate the flexibility and power of our approach by comparing the competitive ratio of several on-line algorithms, including D(over), that have been proposed in the past, for various tasksets. Our experimental results reveal that none of these algorithms is universally optimal, in the sense that there are tasksets where other schedulers provide better performance. Our framework is hence a very useful design tool for selecting optimal algorithms for a given application.
AU - Chatterjee, Krishnendu
AU - Kössler, Alexander
AU - Pavlogiannis, Andreas
AU - Schmid, Ulrich
ID - 5423
SN - 2664-1690
TI - A framework for automated competitive analysis of on-line scheduling of firm-deadline tasks
ER -
TY - GEN
AB - We consider partially observable Markov decision processes (POMDPs), that are a standard framework for robotics applications to model uncertainties present in the real world, with temporal logic specifications. All temporal logic specifications in linear-time temporal logic (LTL) can be expressed as parity objectives. We study the qualitative analysis problem for POMDPs with parity objectives that asks whether there is a controller (policy) to ensure that the objective holds with probability 1 (almost-surely). While the qualitative analysis of POMDPs with parity objectives is undecidable, recent results show that when restricted to finite-memory policies the problem is EXPTIME-complete. While the problem is intractable in theory, we present a practical approach to solve the qualitative analysis problem. We designed several heuristics to deal with the exponential complexity, and have used our implementation on a number of well-known POMDP examples for robotics applications. Our results provide the first practical approach to solve the qualitative analysis of robot motion planning with LTL properties in the presence of uncertainty.
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Gupta, Raghav
AU - Kanodia, Ayush
ID - 5424
SN - 2664-1690
TI - Qualitative analysis of POMDPs with temporal logic specifications for robotics applications
ER -
TY - GEN
AB - We consider partially observable Markov decision processes (POMDPs) with a set of target states and every transition is associated with an integer cost. The optimization objective we study asks to minimize the expected total cost till the target set is reached, while ensuring that the target set is reached almost-surely (with probability 1). We show that for integer costs approximating the optimal cost is undecidable. For positive costs, our results are as follows: (i) we establish matching lower and upper bounds for the optimal cost and the bound is double exponential; (ii) we show that the problem of approximating the optimal cost is decidable and present approximation algorithms developing on the existing algorithms for POMDPs with finite-horizon objectives. While the worst-case running time of our algorithm is double exponential, we also present efficient stopping criteria for the algorithm and show experimentally that it performs well in many examples of interest.
AU - Anonymous, 1
AU - Anonymous, 2
AU - Anonymous, 3
AU - Anonymous, 4
ID - 5425
SN - 2664-1690
TI - Optimal cost almost-sure reachability in POMDPs
ER -
TY - GEN
AB - We consider partially observable Markov decision processes (POMDPs), that are a standard framework for robotics applications to model uncertainties present in the real world, with temporal logic specifications. All temporal logic specifications in linear-time temporal logic (LTL) can be expressed as parity objectives. We study the qualitative analysis problem for POMDPs with parity objectives that asks whether there is a controller (policy) to ensure that the objective holds with probability 1 (almost-surely). While the qualitative analysis of POMDPs with parity objectives is undecidable, recent results show that when restricted to finite-memory policies the problem is EXPTIME-complete. While the problem is intractable in theory, we present a practical approach to solve the qualitative analysis problem. We designed several heuristics to deal with the exponential complexity, and have used our implementation on a number of well-known POMDP examples for robotics applications. Our results provide the first practical approach to solve the qualitative analysis of robot motion planning with LTL properties in the presence of uncertainty.
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Gupta, Raghav
AU - Kanodia, Ayush
ID - 5426
SN - 2664-1690
TI - Qualitative analysis of POMDPs with temporal logic specifications for robotics applications
ER -
TY - GEN
AB - We consider graphs with n nodes together with their tree-decomposition that has b = O ( n ) bags and width t , on the standard RAM computational model with wordsize W = Θ (log n ) . Our contributions are two-fold: Our first contribution is an algorithm that given a graph and its tree-decomposition as input, computes a binary and balanced tree-decomposition of width at most 4 · t + 3 of the graph in O ( b ) time and space, improving a long-standing (from 1992) bound of O ( n · log n ) time for constant treewidth graphs. Our second contribution is on reachability queries for low treewidth graphs. We build on our tree-balancing algorithm and present a data-structure for graph reachability that requires O ( n · t 2 ) preprocessing time, O ( n · t ) space, and O ( d t/ log n e ) time for pair queries, and O ( n · t · log t/ log n ) time for single-source queries. For constant t our data-structure uses O ( n ) time for preprocessing, O (1) time for pair queries, and O ( n/ log n ) time for single-source queries. This is (asymptotically) optimal and is faster than DFS/BFS when answering more than a constant number of single-source queries.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Pavlogiannis, Andreas
ID - 5427
SN - 2664-1690
TI - Optimal tree-decomposition balancing and reachability on low treewidth graphs
ER -
TY - GEN
AB - Simulation is an attractive alternative for language inclusion for automata as it is an under-approximation of language inclusion, but usually has much lower complexity. For non-deterministic automata, while language inclusion is PSPACE-complete, simulation can be computed in polynomial time. Simulation has also been extended in two orthogonal directions, namely, (1) fair simulation, for simulation over specified set of infinite runs; and (2) quantitative simulation, for simulation between weighted automata. Again, while fair trace inclusion is PSPACE-complete, fair simulation can be computed in polynomial time. For weighted automata, the (quantitative) language inclusion problem is undecidable for mean-payoff automata and the decidability is open for discounted-sum automata, whereas the (quantitative) simulation reduce to mean-payoff games and discounted-sum games, which admit pseudo-polynomial time algorithms.
In this work, we study (quantitative) simulation for weighted automata with Büchi acceptance conditions, i.e., we generalize fair simulation from non-weighted automata to weighted automata. We show that imposing Büchi acceptance conditions on weighted automata changes many fundamental properties of the simulation games. For example, whereas for mean-payoff and discounted-sum games, the players do not need memory to play optimally; we show in contrast that for simulation games with Büchi acceptance conditions, (i) for mean-payoff objectives, optimal strategies for both players require infinite memory in general, and (ii) for discounted-sum objectives, optimal strategies need not exist for both players. While the simulation games with Büchi acceptance conditions are more complicated (e.g., due to infinite-memory requirements for mean-payoff objectives) as compared to their counterpart without Büchi acceptance conditions, we still present pseudo-polynomial time algorithms to solve simulation games with Büchi acceptance conditions for both weighted mean-payoff and weighted discounted-sum automata.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Otop, Jan
AU - Velner, Yaron
ID - 5428
SN - 2664-1690
TI - Quantitative fair simulation games
ER -
TY - GEN
AB - In this work we present a flexible tool for tumor progression, which simulates the evolutionary dynamics of cancer. Tumor progression implements a multi-type branching process where the key parameters are the fitness landscape, the mutation rate, and the average time of cell division. The fitness of a cancer cell depends on the mutations it has accumulated. The input to our tool could be any fitness landscape, mutation rate, and cell division time, and the tool produces the growth dynamics and all relevant statistics.
AU - Reiter, Johannes
AU - Bozic, Ivana
AU - Chatterjee, Krishnendu
AU - Nowak, Martin
ID - 5399
SN - 2664-1690
TI - TTP: Tool for Tumor Progression
ER -
TY - GEN
AB - We consider partially observable Markov decision processes (POMDPs) with ω-regular conditions specified as parity objectives. The class of ω-regular languages extends regular languages to infinite strings and provides a robust specification language to express all properties used in verification, and parity objectives are canonical forms to express ω-regular conditions. The qualitative analysis problem given a POMDP and a parity objective asks whether there is a strategy to ensure that the objective is satis- fied with probability 1 (resp. positive probability). While the qualitative analysis problems are known to be undecidable even for very special cases of parity objectives, we establish decidability (with optimal complexity) of the qualitative analysis problems for POMDPs with all parity objectives under finite- memory strategies. We establish asymptotically optimal (exponential) memory bounds and EXPTIME- completeness of the qualitative analysis problems under finite-memory strategies for POMDPs with parity objectives.
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Tracol, Mathieu
ID - 5400
SN - 2664-1690
TI - What is decidable about partially observable Markov decision processes with ω-regular objectives
ER -
TY - GEN
AB - Linearizability requires that the outcome of calls by competing threads to a concurrent data structure is the same as some sequential execution where each thread has exclusive access to the data structure. In an ordered data structure, such as a queue or a stack, linearizability is ensured by requiring threads commit in the order dictated by the sequential semantics of the data structure; e.g., in a concurrent queue implementation a dequeue can only remove the oldest element.
In this paper, we investigate the impact of this strict ordering, by comparing what linearizability allows to what existing implementations do. We first give an operational definition for linearizability which allows us to build the most general linearizable implementation as a transition system for any given sequential specification. We then use this operational definition to categorize linearizable implementations based on whether they are bound or free. In a bound implementation, whenever all threads observe the same logical state, the updates to the logical state and the temporal order of commits coincide. All existing queue implementations we know of are bound. We then proceed to present, to the best of our knowledge, the first ever free queue implementation. Our experiments show that free implementations have the potential for better performance by suffering less from contention.
AU - Henzinger, Thomas A
AU - Sezgin, Ali
ID - 5402
SN - 2664-1690
TI - How free is your linearizable concurrent data structure?
ER -
TY - GEN
AB - We consider concurrent games played by two-players on a finite state graph, where in every round the players simultaneously choose a move, and the current state along with the joint moves determine the successor state. We study the most fundamental objective for concurrent games, namely, mean-payoff or limit-average objective, where a reward is associated to every transition, and the goal of player 1 is to maximize the long-run average of the rewards, and the objective of player 2 is strictly the opposite (i.e., the games are zero-sum). The path constraint for player 1 could be qualitative, i.e., the mean-payoff is the maximal reward, or arbitrarily close to it; or quantitative, i.e., a given threshold between the minimal and maximal reward. We consider the computation of the almost-sure (resp. positive) winning sets, where player 1 can ensure that the path constraint is satisfied with probability 1 (resp. positive probability). Almost-sure winning with qualitative constraint exactly corresponds to the question whether there exists a strategy to ensure that the payoff is the maximal reward of the game. Our main results for qualitative path constraints are as follows: (1) we establish qualitative determinacy results that show for every state either player 1 has a strategy to ensure almost-sure (resp. positive) winning against all player-2 strategies or player 2 has a spoiling strategy to falsify almost-sure (resp. positive) winning against all player-1 strategies; (2) we present optimal strategy complexity results that precisely characterize the classes of strategies required for almost-sure and positive winning for both players; and (3) we present quadratic time algorithms to compute the almost-sure and the positive winning sets, matching the best known bound of the algorithms for much simpler problems (such as reachability objectives). For quantitative constraints we show that a polynomial time solution for the almost-sure or the positive winning set would imply a solution to a long-standing open problem (of solving the value problem of mean-payoff games) that is not known to be in polynomial time.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
ID - 5403
SN - 2664-1690
TI - Qualitative analysis of concurrent mean-payoff games
ER -
TY - GEN
AB - We study finite-state two-player (zero-sum) concurrent mean-payoff games played on a graph. We focus on the important sub-class of ergodic games where all states are visited infinitely often with probability 1. The algorithmic study of ergodic games was initiated in a seminal work of Hoffman and Karp in 1966, but all basic complexity questions have remained unresolved. Our main results for ergodic games are as follows: We establish (1) an optimal exponential bound on the patience of stationary strategies (where patience of a distribution is the inverse of the smallest positive probability and represents a complexity measure of a stationary strategy); (2) the approximation problem lie in FNP; (3) the approximation problem is at least as hard as the decision problem for simple stochastic games (for which NP and coNP is the long-standing best known bound). We show that the exact value can be expressed in the existential theory of the reals, and also establish square-root sum hardness for a related class of games.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
ID - 5404
SN - 2664-1690
TI - The complexity of ergodic games
ER -
TY - GEN
AB - The theory of graph games is the foundation for modeling and synthesizing reactive processes. In the synthesis of stochastic processes, we use 2-1/2-player games where some transitions of the game graph are controlled by two adversarial players, the System and the Environment, and the other transitions are determined probabilistically. We consider 2-1/2-player games where the objective of the System is the conjunction of a qualitative objective (specified as a parity condition) and a quantitative objective (specified as a mean-payoff condition). We establish that the problem of deciding whether the System can ensure that the probability to satisfy the mean-payoff parity objective is at least a given threshold is in NP ∩ coNP, matching the best known bound in the special case of 2-player games (where all transitions are deterministic) with only parity objectives, or with only mean-payoff objectives. We present an algorithm running
in time O(d · n^{2d}·MeanGame) to compute the set of almost-sure winning states from which the objective
can be ensured with probability 1, where n is the number of states of the game, d the number of priorities
of the parity objective, and MeanGame is the complexity to compute the set of almost-sure winning states
in 2-1/2-player mean-payoff games. Our results are useful in the synthesis of stochastic reactive systems
with both functional requirement (given as a qualitative objective) and performance requirement (given
as a quantitative objective).
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Gimbert, Hugo
AU - Oualhadj, Youssouf
ID - 5405
SN - 2664-1690
TI - Perfect-information stochastic mean-payoff parity games
ER -
TY - GEN
AB - We consider the distributed synthesis problem fortemporal logic specifications. Traditionally, the problem has been studied for LTL, and the previous results show that the problem is decidable iff there is no information fork in the architecture. We consider the problem for fragments of LTLand our main results are as follows: (1) We show that the problem is undecidable for architectures with information forks even for the fragment of LTL with temporal operators restricted to next and eventually. (2) For specifications restricted to globally along with non-nested next operators, we establish decidability (in EXPSPACE) for star architectures where the processes receive disjoint inputs, whereas we establish undecidability for architectures containing an information fork-meet structure. (3)Finally, we consider LTL without the next operator, and establish decidability (NEXPTIME-complete) for all architectures for a fragment that consists of a set of safety assumptions, and a set of guarantees where each guarantee is a safety, reachability, or liveness condition.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Otop, Jan
AU - Pavlogiannis, Andreas
ID - 5406
SN - 2664-1690
TI - Distributed synthesis for LTL Fragments
ER -
TY - GEN
AB - We consider two-player partial-observation stochastic games where player 1 has partial observation and player 2 has perfect observation. The winning condition we study are omega-regular conditions specified as parity objectives. The qualitative analysis problem given a partial-observation stochastic game and a parity objective asks whether there is a strategy to ensure that the objective is satisfied with probability 1 (resp. positive probability). While the qualitative analysis problems are known to be undecidable even for very special cases of parity objectives, they were shown to be decidable in 2EXPTIME under finite-memory strategies. We improve the complexity and show that the qualitative analysis problems for partial-observation stochastic parity games under finite-memory strategies are
EXPTIME-complete; and also establish optimal (exponential) memory bounds for finite-memory strategies required for qualitative analysis.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Nain, Sumit
AU - Vardi, Moshe
ID - 5408
SN - 2664-1690
TI - The complexity of partial-observation stochastic parity games with finite-memory strategies
ER -
TY - GEN
AB - The edit distance between two (untimed) traces is the minimum cost of a sequence of edit operations (insertion, deletion, or substitution) needed to transform one trace to the other. Edit distances have been extensively studied in the untimed setting, and form the basis for approximate matching of sequences in different domains such as coding theory, parsing, and speech recognition.
In this paper, we lift the study of edit distances from untimed languages to the timed setting. We define an edit distance between timed words which incorporates both the edit distance between the untimed words and the absolute difference in timestamps. Our edit distance between two timed words is computable in polynomial time. Further, we show that the edit distance between a timed word and a timed language generated by a timed automaton, defined as the edit distance between the word and the closest word in the language, is PSPACE-complete. While computing the edit distance between two timed automata is undecidable, we show that the approximate version, where we decide if the edit distance between two timed automata is either less than a given parameter or more than delta away from the parameter, for delta>0, can be solved in exponential space and is EXPSPACE-hard. Our definitions and techniques can be generalized to the setting of hybrid systems, and we show analogous decidability results for rectangular automata.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Majumdar, Rupak
ID - 5409
SN - 2664-1690
TI - Edit distance for timed automata
ER -
TY - GEN
AB - Board games, like Tic-Tac-Toe and CONNECT-4, play an important role not only in development of mathematical and logical skills, but also in emotional and social development. In this paper, we address the problem of generating targeted starting positions for such games. This can facilitate new approaches for bringing novice players to mastery, and also leads to discovery of interesting game variants.
Our approach generates starting states of varying hardness levels for player 1 in a two-player board game, given rules of the board game, the desired number of steps required for player 1 to win, and the expertise levels of the two players. Our approach leverages symbolic methods and iterative simulation to efficiently search the extremely large state space. We present experimental results that include discovery of states of varying hardness levels for several simple grid-based board games. Also, the presence of such states for standard game variants like Tic-Tac-Toe on board size 4x4 opens up new games to be played that have not been played for ages since the default start state is heavily biased.
AU - Ahmed, Umair
AU - Chatterjee, Krishnendu
AU - Gulwani, Sumit
ID - 5410
SN - 2664-1690
TI - Automatic generation of alternative starting positions for traditional board games
ER -
TY - GEN
AB - In order to guarantee that each method of a data structure updates the logical state exactly once, al-most all non-blocking implementations employ Compare-And-Swap (CAS) based synchronization. For FIFO queue implementations this translates into concurrent enqueue or dequeue methods competing among themselves to update the same variable, the tail or the head, respectively, leading to high contention and poor scalability. Recent non-blocking queue implementations try to alleviate high contentionby increasing the number of contention points, all the while using CAS-based synchronization. Furthermore, obtaining a wait-free implementation with competition is achieved by additional synchronization which leads to further degradation of performance.In this paper we formalize the notion of competitiveness of a synchronizing statement which can beused as a measure for the scalability of concurrent implementations. We present a new queue implementation, the Speculative Pairing (SP) queue, which, as we show, decreases competitiveness by using Fetch-And-Increment (FAI) instead of CAS. We prove that the SP queue is linearizable and lock-free.We also show that replacing CAS with FAI leads to wait-freedom for dequeue methods without an adverse effect on performance. In fact, our experiments suggest that the SP queue can perform and scale better than the state-of-the-art queue implementations.
AU - Henzinger, Thomas A
AU - Payer, Hannes
AU - Sezgin, Ali
ID - 6440
SN - 2664-1690
TI - Replacing competition with cooperation to achieve scalable lock-free FIFO queues
ER -
TY - GEN
AB - Two-player games on graphs are central in many problems in formal verification and program analysis such as synthesis and verification of open systems. In this work we consider solving recursive game graphs (or pushdown game graphs) that can model the control flow of sequential programs with recursion. While pushdown games have been studied before with qualitative objectives, such as reachability and ω-regular objectives, in this work we study for the first time such games with the most well-studied quantitative objective, namely, mean-payoff objectives. In pushdown games two types of strategies are relevant: (1) global strategies, that depend on the entire global history; and (2) modular strategies, that have only local memory and thus do not depend on the context of invocation, but only on the history of the current invocation of the module. Our main results are as follows: (1) One-player pushdown games with mean-payoff objectives under global strategies are decidable in polynomial time. (2) Two- player pushdown games with mean-payoff objectives under global strategies are undecidable. (3) One-player pushdown games with mean-payoff objectives under modular strategies are NP- hard. (4) Two-player pushdown games with mean-payoff objectives under modular strategies can be solved in NP (i.e., both one-player and two-player pushdown games with mean-payoff objectives under modular strategies are NP-complete). We also establish the optimal strategy complexity showing that global strategies for mean-payoff objectives require infinite memory even in one-player pushdown games; and memoryless modular strategies are sufficient in two- player pushdown games. Finally we also show that all the problems have the same complexity if the stack boundedness condition is added, where along with the mean-payoff objective the player must also ensure that the stack height is bounded.
AU - Chatterjee, Krishnendu
AU - Velner, Yaron
ID - 5377
SN - 2664-1690
TI - Mean-payoff pushdown games
ER -
TY - GEN
AB - One central issue in the formal design and analysis of reactive systems is the notion of refinement that asks whether all behaviors of the implementation is allowed by the specification. The local interpretation of behavior leads to the notion of simulation. Alternating transition systems (ATSs) provide a general model for composite reactive systems, and the simulation relation for ATSs is known as alternating simulation. The simulation relation for fair transition systems is called fair simulation. In this work our main contributions are as follows: (1) We present an improved algorithm for fair simulation with Büchi fairness constraints; our algorithm requires O(n3 · m) time as compared to the previous known O(n6)-time algorithm, where n is the number of states and m is the number of transitions. (2) We present a game based algorithm for alternating simulation that requires O(m2)-time as compared to the previous known O((n · m)2)-time algorithm, where n is the number of states and m is the size of transition relation. (3) We present an iterative algorithm for alternating simulation that matches the time complexity of the game based algorithm, but is more space efficient than the game based algorithm.
AU - Chatterjee, Krishnendu
AU - Chaubal, Siddhesh
AU - Kamath, Pritish
ID - 5378
SN - 2664-1690
TI - Faster algorithms for alternating refinement relations
ER -
TY - GEN
AB - We consider the problem of inference in agraphical model with binary variables. While in theory it is arguably preferable to compute marginal probabilities, in practice researchers often use MAP inference due to the availability of efficient discrete optimization algorithms. We bridge the gap between the two approaches by introducing the Discrete Marginals technique in which approximate marginals are obtained by minimizing an objective function with unary and pair-wise terms over a discretized domain. This allows the use of techniques originally devel-oped for MAP-MRF inference and learning. We explore two ways to set up the objective function - by discretizing the Bethe free energy and by learning it from training data. Experimental results show that for certain types of graphs a learned function can out-perform the Bethe approximation. We also establish a link between the Bethe free energy and submodular functions.
AU - Korc, Filip
AU - Kolmogorov, Vladimir
AU - Lampert, Christoph
ID - 5396
SN - 2664-1690
TI - Approximating marginals using discrete energy minimization
ER -
TY - GEN
AB - Computing the winning set for Büchi objectives in alternating games on graphs is a central problem in computer aided verification with a large number of applications. The long standing best known upper bound for solving the problem is ̃O(n·m), where n is the number of vertices and m is the number of edges in the graph. We are the first to break the ̃O(n·m) boundary by presenting a new technique that reduces the running time to O(n2). This bound also leads to O(n2) time algorithms for computing the set of almost-sure winning vertices for Büchi objectives (1) in alternating games with probabilistic transitions (improving an earlier bound of O(n·m)), (2) in concurrent graph games with constant actions (improving an earlier bound of O(n3)), and (3) in Markov decision processes (improving for m > n4/3 an earlier bound of O(min(m1.5, m·n2/3)). We also show that the same technique can be used to compute the maximal end-component decomposition of a graph in time O(n2), which is an improvement over earlier bounds for m > n4/3. Finally, we show how to maintain the winning set for Büchi objectives in alternating games under a sequence of edge insertions or a sequence of edge deletions in O(n) amortized time per operation. This is the first dynamic algorithm for this problem.
AU - Chatterjee, Krishnendu
AU - Henzinger, Monika
ID - 5379
SN - 2664-1690
TI - An O(n2) time algorithm for alternating Büchi games
ER -
TY - GEN
AB - We consider 2-player games played on a finite state space for an infinite number of rounds. The games are concurrent: in each round, the two players (player 1 and player 2) choose their moves independently and simultaneously; the current state and the two moves determine the successor state. We study concurrent games with ω-regular winning conditions specified as parity objectives. We consider the qualitative analysis problems: the computation of the almost-sure and limit-sure winning set of states, where player 1 can ensure to win with probability 1 and with probability arbitrarily close to 1, respectively. In general the almost-sure and limit-sure winning strategies require both infinite-memory as well as infinite-precision (to describe probabilities). We study the bounded-rationality problem for qualitative analysis of concurrent parity games, where the strategy set for player 1 is restricted to bounded-resource strategies. In terms of precision, strategies can be deterministic, uniform, finite-precision or infinite-precision; and in terms of memory, strategies can be memoryless, finite-memory or infinite-memory. We present a precise and complete characterization of the qualitative winning sets for all combinations of classes of strategies. In particular, we show that uniform memoryless strategies are as powerful as finite-precision infinite-memory strategies, and infinite-precision memoryless strategies are as powerful as infinite-precision finite-memory strategies. We show that the winning sets can be computed in O(n2d+3) time, where n is the size of the game structure and 2d is the number of priorities (or colors), and our algorithms are symbolic. The membership problem of whether a state belongs to a winning set can be decided in NP ∩ coNP. While this complexity is the same as for the simpler class of turn-based parity games, where in each state only one of the two players has a choice of moves, our algorithms,that are obtained by characterization of the winning sets as μ-calculus formulas, are considerably more involved than those for turn-based games.
AU - Chatterjee, Krishnendu
ID - 5380
SN - 2664-1690
TI - Bounded rationality in concurrent parity games
ER -
TY - GEN
AB - In two-player finite-state stochastic games of partial obser- vation on graphs, in every state of the graph, the players simultaneously choose an action, and their joint actions determine a probability distri- bution over the successor states. The game is played for infinitely many rounds and thus the players construct an infinite path in the graph. We consider reachability objectives where the first player tries to ensure a target state to be visited almost-surely (i.e., with probability 1) or pos- itively (i.e., with positive probability), no matter the strategy of the second player.
We classify such games according to the information and to the power of randomization available to the players. On the basis of information, the game can be one-sided with either (a) player 1, or (b) player 2 having partial observation (and the other player has perfect observation), or two- sided with (c) both players having partial observation. On the basis of randomization, (a) the players may not be allowed to use randomization (pure strategies), or (b) they may choose a probability distribution over actions but the actual random choice is external and not visible to the player (actions invisible), or (c) they may use full randomization.
Our main results for pure strategies are as follows: (1) For one-sided games with player 2 perfect observation we show that (in contrast to full randomized strategies) belief-based (subset-construction based) strate- gies are not sufficient, and present an exponential upper bound on mem- ory both for almost-sure and positive winning strategies; we show that the problem of deciding the existence of almost-sure and positive winning strategies for player 1 is EXPTIME-complete and present symbolic algo- rithms that avoid the explicit exponential construction. (2) For one-sided games with player 1 perfect observation we show that non-elementary memory is both necessary and sufficient for both almost-sure and posi- tive winning strategies. (3) We show that for the general (two-sided) case finite-memory strategies are sufficient for both positive and almost-sure winning, and at least non-elementary memory is required. We establish the equivalence of the almost-sure winning problems for pure strategies and for randomized strategies with actions invisible. Our equivalence re- sult exhibit serious flaws in previous results in the literature: we show a non-elementary memory lower bound for almost-sure winning whereas an exponential upper bound was previously claimed.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
ID - 5381
SN - 2664-1690
TI - Partial-observation stochastic games: How to win when belief fails
ER -
TY - GEN
AB - We consider two-player stochastic games played on a finite state space for an infinite num- ber of rounds. The games are concurrent: in each round, the two players (player 1 and player 2) choose their moves independently and simultaneously; the current state and the two moves determine a probability distribution over the successor states. We also consider the important special case of turn-based stochastic games where players make moves in turns, rather than concurrently. We study concurrent games with ω-regular winning conditions specified as parity objectives. The value for player 1 for a parity objective is the maximal probability with which the player can guarantee the satisfaction of the objective against all strategies of the opponent. We study the problem of continuity and robustness of the value function in concurrent and turn-based stochastic parity games with respect to imprecision in the transition probabilities. We present quantitative bounds on the difference of the value function (in terms of the imprecision of the transition probabilities) and show the value continuity for structurally equivalent concurrent games (two games are structurally equivalent if the support of the transition func- tion is same and the probabilities differ). We also show robustness of optimal strategies for structurally equivalent turn-based stochastic parity games. Finally we show that the value continuity property breaks without the structurally equivalent assumption (even for Markov chains) and show that our quantitative bound is asymptotically optimal. Hence our results are tight (the assumption is both necessary and sufficient) and optimal (our quantitative bound is asymptotically optimal).
AU - Chatterjee, Krishnendu
ID - 5382
SN - 2664-1690
TI - Robustness of structurally equivalent concurrent parity games
ER -
TY - GEN
AB - We present a new decidable logic called TREX for expressing constraints about imperative tree data structures. In particular, TREX supports a transitive closure operator that can express reachability constraints, which often appear in data structure invariants. We show that our logic is closed under weakest precondition computation, which enables its use for automated software verification. We further show that satisfiability of formulas in TREX is decidable in NP. The low complexity makes it an attractive alternative to more expensive logics such as monadic second-order logic (MSOL) over trees, which have been traditionally used for reasoning about tree data structures.
AU - Wies, Thomas
AU - Muñiz, Marco
AU - Kuncak, Viktor
ID - 5383
SN - 2664-1690
TI - On an efficient decision procedure for imperative tree data structures
ER -
TY - GEN
AB - We consider probabilistic automata on infinite words with acceptance defined by parity conditions. We consider three qualitative decision problems: (i) the positive decision problem asks whether there is a word that is accepted with positive probability; (ii) the almost decision problem asks whether there is a word that is accepted with probability 1; and (iii) the limit decision problem asks whether for every ε > 0 there is a word that is accepted with probability at least 1 − ε. We unify and generalize several decidability results for probabilistic automata over infinite words, and identify a robust (closed under union and intersection) subclass of probabilistic automata for which all the qualitative decision problems are decidable for parity conditions. We also show that if the input words are restricted to lasso shape words, then the positive and almost problems are decidable for all probabilistic automata with parity conditions.
AU - Chatterjee, Krishnendu
AU - Tracol, Mathieu
ID - 5384
SN - 2664-1690
TI - Decidable problems for probabilistic automata on infinite words
ER -
TY - GEN
AB - There is recently a significant effort to add quantitative objectives to formal verification and synthesis. We introduce and investigate the extension of temporal logics with quantitative atomic assertions, aiming for a general and flexible framework for quantitative-oriented specifications. In the heart of quantitative objectives lies the accumulation of values along a computation. It is either the accumulated summation, as with the energy objectives, or the accumulated average, as with the mean-payoff objectives. We investigate the extension of temporal logics with the prefix-accumulation assertions Sum(v) ≥ c and Avg(v) ≥ c, where v is a numeric variable of the system, c is a constant rational number, and Sum(v) and Avg(v) denote the accumulated sum and average of the values of v from the beginning of the computation up to the current point of time. We also allow the path-accumulation assertions LimInfAvg(v) ≥ c and LimSupAvg(v) ≥ c, referring to the average value along an entire computation. We study the border of decidability for extensions of various temporal logics. In particular, we show that extending the fragment of CTL that has only the EX, EF, AX, and AG temporal modalities by prefix-accumulation assertions and extending LTL with path-accumulation assertions, result in temporal logics whose model-checking problem is decidable. The extended logics allow to significantly extend the currently known energy and mean-payoff objectives. Moreover, the prefix-accumulation assertions may be refined with “controlled-accumulation”, allowing, for example, to specify constraints on the average waiting time between a request and a grant. On the negative side, we show that the fragment we point to is, in a sense, the maximal logic whose extension with prefix-accumulation assertions permits a decidable model-checking procedure. Extending a temporal logic that has the EG or EU modalities, and in particular CTL and LTL, makes the problem undecidable.
AU - Boker, Udi
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Kupferman, Orna
ID - 5385
SN - 2664-1690
TI - Temporal specifications with accumulative values
ER -
TY - GEN
AB - We introduce TopoCut: a new way to integrate knowledge about topological properties (TPs) into random field image segmentation model. Instead of including TPs as additional constraints during minimization of the energy function, we devise an efficient algorithm for modifying the unary potentials such that the resulting segmentation is guaranteed with the desired properties. Our method is more flexible in the sense that it handles more topology constraints than previous methods, which were only able to enforce pairwise or global connectivity. In particular, our method is very fast, making it for the first time possible to enforce global topological properties in practical image segmentation tasks.
AU - Chen, Chao
AU - Freedman, Daniel
AU - Lampert, Christoph
ID - 5386
SN - 2664-1690
TI - Enforcing topological constraints in random field image segmentation
ER -
TY - GEN
AB - We consider Markov Decision Processes (MDPs) with mean-payoff parity and energy parity objectives. In system design, the parity objective is used to encode ω-regular specifications, and the mean-payoff and energy objectives can be used to model quantitative resource constraints. The energy condition re- quires that the resource level never drops below 0, and the mean-payoff condi- tion requires that the limit-average value of the resource consumption is within a threshold. While these two (energy and mean-payoff) classical conditions are equivalent for two-player games, we show that they differ for MDPs. We show that the problem of deciding whether a state is almost-sure winning (i.e., winning with probability 1) in energy parity MDPs is in NP ∩ coNP, while for mean- payoff parity MDPs, the problem is solvable in polynomial time, improving a recent PSPACE bound.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
ID - 5387
SN - 2664-1690
TI - Energy and mean-payoff parity Markov decision processes
ER -
TY - GEN
AB - We present an algorithmic method for the synthesis of concurrent programs that are optimal with respect to quantitative performance measures. The input consists of a sequential sketch, that is, a program that does not contain synchronization constructs, and of a parametric performance model that assigns costs to actions such as locking, context switching, and idling. The quantitative synthesis problem is to automatically introduce synchronization constructs into the sequential sketch so that both correctness is guaranteed and worst-case (or average-case) performance is optimized. Correctness is formalized as race freedom or linearizability.
We show that for worst-case performance, the problem can be modeled
as a 2-player graph game with quantitative (limit-average) objectives, and
for average-case performance, as a 2 1/2 -player graph game (with probabilistic transitions). In both cases, the optimal correct program is derived from an optimal strategy in the corresponding quantitative game. We prove that the respective game problems are computationally expensive (NP-complete), and present several techniques that overcome the theoretical difficulty in cases of concurrent programs of practical interest.
We have implemented a prototype tool and used it for the automatic syn- thesis of programs that access a concurrent list. For certain parameter val- ues, our method automatically synthesizes various classical synchronization schemes for implementing a concurrent list, such as fine-grained locking or a lazy algorithm. For other parameter values, a new, hybrid synchronization style is synthesized, which uses both the lazy approach and coarse-grained locks (instead of standard fine-grained locks). The trade-off occurs because while fine-grained locking tends to decrease the cost that is due to waiting for locks, it increases cache size requirements.
AU - Chatterjee, Krishnendu
AU - Cerny, Pavol
AU - Henzinger, Thomas A
AU - Radhakrishna, Arjun
AU - Singh, Rohit
ID - 5388
SN - 2664-1690
TI - Quantitative synthesis for concurrent programs
ER -
TY - GEN
AB - Boolean notions of correctness are formalized by preorders on systems. Quantitative measures of correctness can be formalized by real-valued distance functions between systems, where the distance between implementation and specification provides a measure of “fit” or “desirability.” We extend the simulation preorder to the quantitative setting, by making each player of a simulation game pay a certain price for her choices. We use the resulting games with quantitative objectives to define three different simulation distances. The correctness distance measures how much the specification must be changed in order to be satisfied by the implementation. The coverage distance measures how much the im- plementation restricts the degrees of freedom offered by the specification. The robustness distance measures how much a system can deviate from the implementation description without violating the specification. We consider these distances for safety as well as liveness specifications. The distances can be computed in polynomial time for safety specifications, and for liveness specifications given by weak fairness constraints. We show that the distance functions satisfy the triangle inequality, that the distance between two systems does not increase under parallel composition with a third system, and that the distance between two systems can be bounded from above and below by distances between abstractions of the two systems. These properties suggest that our simulation distances provide an appropriate basis for a quantitative theory of discrete systems. We also demonstrate how the robustness distance can be used to measure how many transmission errors are tolerated by error correcting codes.
AU - Cerny, Pavol
AU - Henzinger, Thomas A
AU - Radhakrishna, Arjun
ID - 5389
SN - 2664-1690
TI - Simulation distances
ER -
TY - GEN
AB - The class of ω regular languages provide a robust specification language in verification. Every ω-regular condition can be decomposed into a safety part and a liveness part. The liveness part ensures that something good happens “eventually.” Two main strengths of the classical, infinite-limit formulation of liveness are robustness (independence from the granularity of transitions) and simplicity (abstraction of complicated time bounds). However, the classical liveness formulation suffers from the drawback that the time until something good happens may be unbounded. A stronger formulation of liveness, so-called finitary liveness, overcomes this drawback, while still retaining robustness and simplicity. Finitary liveness requires that there exists an unknown, fixed bound b such that something good happens within b transitions. In this work we consider the finitary parity and Streett (fairness) conditions. We present the topological, automata-theoretic and logical characterization of finitary languages defined by finitary parity and Streett conditions. We (a) show that the finitary parity and Streett languages are Σ2-complete; (b) present a complete characterization of the expressive power of various classes of automata with finitary and infinitary conditions (in particular we show that non-deterministic finitary parity and Streett automata cannot be determinized to deterministic finitary parity or Streett automata); and (c) show that the languages defined by non-deterministic finitary parity automata exactly characterize the star-free fragment of ωB-regular languages.
AU - Chatterjee, Krishnendu
AU - Fijalkow, Nathanaël
ID - 5390
SN - 2664-1690
TI - Topological, automata-theoretic and logical characterization of finitary languages
ER -
TY - GEN
AB - Concurrent data structures with fine-grained synchronization are notoriously difficult to implement correctly. The difficulty of reasoning about these implementations does not stem from the number of variables or the program size, but rather from the large number of possible interleavings. These implementations are therefore prime candidates for model checking. We introduce an algorithm for verifying linearizability of singly-linked heap-based concurrent data structures. We consider a model consisting of an unbounded heap where each node consists an element from an unbounded data domain, with a restricted set of operations for testing and updating pointers and data elements. Our main result is that linearizability is decidable for programs that invoke a fixed number of methods, possibly in parallel. This decidable fragment covers many of the common implementation techniques — fine-grained locking, lazy synchronization, and lock-free synchronization. We also show how the technique can be used to verify optimistic implementations with the help of programmer annotations. We developed a verification tool CoLT and evaluated it on a representative sample of Java implementations of the concurrent set data structure. The tool verified linearizability of a number of implementations, found a known error in a lock-free imple- mentation and proved that the corrected version is linearizable.
AU - Cerny, Pavol
AU - Radhakrishna, Arjun
AU - Zufferey, Damien
AU - Chaudhuri, Swarat
AU - Alur, Rajeev
ID - 5391
SN - 2664-1690
TI - Model checking of linearizability of concurrent list implementations
ER -
TY - GEN
AB - We consider probabilistic automata on infinite words with acceptance defined by safety, reachability, Büchi, coBüchi and limit-average conditions. We consider quantitative and qualitative decision problems. We present extensions and adaptations of proofs of [GO09] and present a precise characterization of the decidability and undecidability frontier of the quantitative and qualitative decision problems.
AU - Chatterjee, Krishnendu
ID - 5392
SN - 2664-1690
TI - Probabilistic automata on infinite words: Decidability and undecidability results
ER -
TY - GEN
AB - Gist is a tool that (a) solves the qualitative analysis problem of turn-based probabilistic games with ω-regular objectives; and (b) synthesizes reasonable environment assumptions for synthesis of unrealizable specifications. Our tool provides efficient implementations of several reduction based techniques to solve turn-based probabilistic games, and uses the analysis of turn-based probabilistic games for synthesizing environment assumptions for unrealizable specifications.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Jobstmann, Barbara
AU - Radhakrishna, Arjun
ID - 5393
SN - 2664-1690
TI - Gist: A solver for probabilistic games
ER -
TY - GEN
AB - We consider two-player games played on graphs with request-response and finitary Streett objectives. We show these games are PSPACE-hard, improving the previous known NP-hardness. We also improve the lower bounds on memory required by the winning strategies for the players.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Horn, Florian
ID - 5394
SN - 2664-1690
TI - Improved lower bounds for request-response and finitary Streett games
ER -
TY - GEN
AB - We study observation-based strategies for partially-observable Markov decision processes (POMDPs) with omega-regular objectives. An observation-based strategy relies on partial information about the history of a play, namely, on the past sequence of observa- tions. We consider the qualitative analysis problem: given a POMDP with an omega-regular objective, whether there is an observation-based strategy to achieve the objective with probability 1 (almost-sure winning), or with positive probability (positive winning). Our main results are twofold. First, we present a complete picture of the computational complexity of the qualitative analysis of POMDPs with parity objectives (a canonical form to express omega-regular objectives) and its subclasses. Our contribution consists in establishing several upper and lower bounds that were not known in literature. Second, we present optimal bounds (matching upper and lower bounds) on the memory required by pure and randomized observation-based strategies for the qualitative analysis of POMDPs with parity objectives and its subclasses.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Henzinger, Thomas A
ID - 5395
SN - 2664-1690
TI - Qualitative analysis of partially-observable Markov decision processes
ER -