@misc{5457,
abstract = {We consider the problem of expected cost analysis over nondeterministic probabilistic programs, which aims at automated methods for analyzing the resource-usage of such programs. Previous approaches for this problem could only handle nonnegative bounded costs. However, in many scenarios, such as queuing networks or analysis of cryptocurrency protocols, both positive and negative costs are necessary and the costs are unbounded as well.
In this work, we present a sound and efficient approach to obtain polynomial bounds on the expected accumulated cost of nondeterministic probabilistic programs. Our approach can handle (a) general positive and negative costs with bounded updates in variables; and (b) nonnegative costs with general updates to variables. We show that several natural examples which could not be handled by previous approaches are captured in our framework.
Moreover, our approach leads to an efficient polynomial-time algorithm, while no previous approach for cost analysis of probabilistic programs could guarantee polynomial runtime. Finally, we show the effectiveness of our approach by presenting experimental results on a variety of programs, motivated by real-world applications, for which we efficiently synthesize tight resource-usage bounds.},
author = {Anonymous, 1 and Anonymous, 2 and Anonymous, 3 and Anonymous, 4 and Anonymous, 5 and Anonymous, 6},
issn = {2664-1690},
pages = {27},
publisher = {IST Austria},
title = {{Cost analysis of nondeterministic probabilistic programs}},
year = {2018},
}
@misc{6426,
abstract = {Synchronous programs are easy to specify because the side effects of an operation are finished by the time the invocation of the operation returns to the caller. Asynchronous programs, on the other hand, are difficult to specify because there are side effects due to pending computation scheduled as a result of the invocation of an operation. They are also difficult to verify because of the large number of possible interleavings of concurrent asynchronous computation threads. We show that specifications and correctness proofs for asynchronous programs can be structured by introducing the fiction, for proof purposes, that intermediate, non-quiescent states of asynchronous operations can be ignored. Then, the task of specification becomes relatively simple and the task of verification can be naturally decomposed into smaller sub-tasks. The sub-tasks iteratively summarize, guided by the structure of an asynchronous program, the atomic effect of non-atomic operations and the synchronous effect of asynchronous operations. This structuring of specifications and proofs corresponds to the introduction of multiple layers of stepwise refinement for asynchronous programs. We present the first proof rule, called synchronization, to reduce asynchronous invocations on a lower layer to synchronous invocations on a higher layer. We implemented our proof method in CIVL and evaluated it on a collection of benchmark programs.},
author = {Henzinger, Thomas A and Kragl, Bernhard and Qadeer, Shaz},
issn = {2664-1690},
pages = {28},
publisher = {IST Austria},
title = {{Synchronizing the asynchronous}},
doi = {10.15479/AT:IST-2018-853-v2-2},
year = {2017},
}
@misc{5455,
abstract = {A fundamental algorithmic problem at the heart of static analysis is Dyck reachability. The input is a graphwhere the edges are labeled with different types of opening and closing parentheses, and the reachabilityinformation is computed via paths whose parentheses are properly matched. We present new results for Dyckreachability problems with applications to alias analysis and data-dependence analysis. Our main contributions,that include improved upper bounds as well as lower bounds that establish optimality guarantees, are asfollows:First, we consider Dyck reachability on bidirected graphs, which is the standard way of performing field-sensitive points-to analysis. Given a bidirected graph withnnodes andmedges, we present: (i) an algorithmwith worst-case running timeO(m+n·α(n)), whereα(n)is the inverse Ackermann function, improving thepreviously knownO(n2)time bound; (ii) a matching lower bound that shows that our algorithm is optimalwrt to worst-case complexity; and (iii) an optimal average-case upper bound ofO(m)time, improving thepreviously knownO(m·logn)bound.Second, we consider the problem of context-sensitive data-dependence analysis, where the task is to obtainanalysis summaries of library code in the presence of callbacks. Our algorithm preprocesses libraries in almostlinear time, after which the contribution of the library in the complexity of the client analysis is only linear,and only wrt the number of call sites.Third, we prove that combinatorial algorithms for Dyck reachability on general graphs with truly sub-cubic bounds cannot be obtained without obtaining sub-cubic combinatorial algorithms for Boolean MatrixMultiplication, which is a long-standing open problem. Thus we establish that the existing combinatorialalgorithms for Dyck reachability are (conditionally) optimal for general graphs. We also show that the samehardness holds for graphs of constant treewidth.Finally, we provide a prototype implementation of our algorithms for both alias analysis and data-dependenceanalysis. Our experimental evaluation demonstrates that the new algorithms significantly outperform allexisting methods on the two problems, over real-world benchmarks.},
author = {Chatterjee, Krishnendu and Choudhary, Bhavya and Pavlogiannis, Andreas},
issn = {2664-1690},
pages = {37},
publisher = {IST Austria},
title = {{Optimal Dyck reachability for data-dependence and alias analysis}},
doi = {10.15479/AT:IST-2017-870-v1-1},
year = {2017},
}
@misc{5456,
abstract = {We present a new dynamic partial-order reduction method for stateless model checking of concurrent programs. A common approach for exploring program behaviors relies on enumerating the traces of the program, without storing the visited states (aka stateless exploration). As the number of distinct traces grows exponentially, dynamic partial-order reduction (DPOR) techniques have been successfully used to partition the space of traces into equivalence classes (Mazurkiewicz partitioning), with the goal of exploring only few representative traces from each class.
We introduce a new equivalence on traces under sequential consistency semantics, which we call the observation equivalence. Two traces are observationally equivalent if every read event observes the same write event in both traces. While the traditional Mazurkiewicz equivalence is control-centric, our new definition is data-centric. We show that our observation equivalence is coarser than the Mazurkiewicz equivalence, and in many cases even exponentially coarser. We devise a DPOR exploration of the trace space, called data-centric DPOR, based on the observation equivalence.
1. For acyclic architectures, our algorithm is guaranteed to explore exactly one representative trace from each observation class, while spending polynomial time per class. Hence, our algorithm is optimal wrt the observation equivalence, and in several cases explores exponentially fewer traces than any enumerative method based on the Mazurkiewicz equivalence.
2. For cyclic architectures, we consider an equivalence between traces which is finer than the observation equivalence; but coarser than the Mazurkiewicz equivalence, and in some cases is exponentially coarser. Our data-centric DPOR algorithm remains optimal under this trace equivalence.
Finally, we perform a basic experimental comparison between the existing Mazurkiewicz-based DPOR and our data-centric DPOR on a set of academic benchmarks. Our results show a significant reduction in both running time and the number of explored equivalence classes.},
author = {Chalupa, Marek and Chatterjee, Krishnendu and Pavlogiannis, Andreas and Sinha, Nishant and Vaidya, Kapil},
issn = {2664-1690},
pages = {36},
publisher = {IST Austria},
title = {{Data-centric dynamic partial order reduction}},
doi = {10.15479/AT:IST-2017-872-v1-1},
year = {2017},
}
@misc{5447,
abstract = {We consider the problem of developing automated techniques to aid the average-case complexity analysis of programs. Several classical textbook algorithms have quite efficient average-case complexity, whereas the corresponding worst-case bounds are either inefficient (e.g., QUICK-SORT), or completely ineffective (e.g., COUPONCOLLECTOR). Since the main focus of average-case analysis is to obtain efficient bounds, we consider bounds that are either logarithmic,
linear, or almost-linear (O(log n), O(n), O(n · log n),
respectively, where n represents the size of the input). Our main contribution is a sound approach for deriving such average-case bounds for randomized recursive programs. Our approach is efficient (a simple linear-time algorithm), and it is based on (a) the analysis of recurrence relations induced by randomized algorithms, and (b) a guess-and-check technique. Our approach can infer the asymptotically optimal average-case bounds for classical randomized algorithms, including RANDOMIZED-SEARCH, QUICKSORT, QUICK-SELECT, COUPON-COLLECTOR, where the worstcase
bounds are either inefficient (such as linear as compared to logarithmic of average-case, or quadratic as compared to linear or almost-linear of average-case), or ineffective. We have implemented our approach, and the experimental results show that we obtain the bounds efficiently for various classical algorithms.},
author = {Anonymous, 1 and Anonymous, 2 and Anonymous, 3},
issn = {2664-1690},
pages = {20},
publisher = {IST Austria},
title = {{Average-case analysis of programs: Automated recurrence analysis for almost-linear bounds}},
year = {2016},
}
@misc{5448,
abstract = {We present a new dynamic partial-order reduction method for stateless model checking of concurrent programs. A common approach for exploring program behaviors relies on enumerating the traces of the program, without storing the visited states (aka stateless exploration). As the number of distinct traces grows exponentially, dynamic partial-order reduction (DPOR) techniques have been successfully used to partition the space of traces into equivalence classes (Mazurkiewicz partitioning), with the goal of exploring only few representative traces from each class.
We introduce a new equivalence on traces under sequential consistency semantics, which we call the observation equivalence. Two traces are observationally equivalent if every read event observes the same write event in both traces. While the traditional Mazurkiewicz equivalence is control-centric, our new definition is data-centric. We show that our observation equivalence is coarser than the Mazurkiewicz equivalence, and in many cases even exponentially coarser. We devise a DPOR exploration of the trace space, called data-centric DPOR, based on the observation equivalence.
1. For acyclic architectures, our algorithm is guaranteed to explore exactly one representative trace from each observation class, while spending polynomial time per class. Hence, our algorithm is optimal wrt the observation equivalence, and in several cases explores exponentially fewer traces than any enumerative method based on the Mazurkiewicz equivalence.
2. For cyclic architectures, we consider an equivalence between traces which is finer than the observation equivalence; but coarser than the Mazurkiewicz equivalence, and in some cases is exponentially coarser. Our data-centric DPOR algorithm remains optimal under this trace equivalence.
Finally, we perform a basic experimental comparison between the existing Mazurkiewicz-based DPOR and our data-centric DPOR on a set of academic benchmarks. Our results show a significant reduction in both running time and the number of explored equivalence classes.},
author = {Anonymous, 1 and Anonymous, 2 and Anonymous, 3 and Anonymous, 4},
issn = {2664-1690},
pages = {20},
publisher = {IST Austria},
title = {{Data-centric dynamic partial order reduction}},
year = {2016},
}
@misc{5451,
author = {Pavlogiannis, Andreas and Tkadlec, Josef and Chatterjee, Krishnendu and Nowak, Martin},
issn = {2664-1690},
pages = {34},
publisher = {IST Austria},
title = {{Strong amplifiers of natural selection}},
doi = {10.15479/AT:IST-2016-728-v1-1},
year = {2016},
}
@misc{5449,
abstract = {The fixation probability is the probability that a new mutant introduced in a homogeneous population eventually takes over the entire population.
The fixation probability is a fundamental quantity of natural selection, and known to depend on the population structure.
Amplifiers of natural selection are population structures which increase the fixation probability of advantageous mutants, as compared to the baseline case of well-mixed populations. In this work we focus on symmetric population structures represented as undirected graphs. In the regime of undirected graphs, the strongest amplifier known has been the Star graph, and the existence of undirected graphs with stronger amplification properties has remained open for over a decade.
In this work we present the Comet and Comet-swarm families of undirected graphs. We show that for a range of fitness values of the mutants, the Comet and Comet-swarm graphs have fixation probability strictly larger than the fixation probability of the Star graph, for fixed population size and at the limit of large populations, respectively.},
author = {Pavlogiannis, Andreas and Tkadlec, Josef and Chatterjee, Krishnendu and Nowak, Martin},
issn = {2664-1690},
pages = {22},
publisher = {IST Austria},
title = {{Amplification on undirected population structures: Comets beat stars}},
doi = {10.15479/AT:IST-2016-648-v1-1},
year = {2016},
}
@misc{5445,
abstract = {We consider the quantitative analysis problem for interprocedural control-flow graphs (ICFGs). The input consists of an ICFG, a positive weight function that assigns every transition a positive integer-valued number, and a labelling of the transitions (events) as good, bad, and neutral events. The weight function assigns to each transition a numerical value that represents ameasure of how good or bad an event is. The quantitative analysis problem asks whether there is a run of the ICFG where the ratio of the sum of the numerical weights of good events versus the sum of weights of bad events in the long-run is at least a given threshold (or equivalently, to compute the maximal ratio among all valid paths in the ICFG). The quantitative analysis problem for ICFGs can be solved in polynomial time, and we present an efficient and practical algorithm for the problem. We show that several problems relevant for static program analysis, such as estimating the worst-case execution time of a program or the average energy consumption of a mobile application, can be modeled in our framework. We have implemented our algorithm as a tool in the Java Soot framework. We demonstrate the effectiveness of our approach with two case studies. First, we show that our framework provides a sound approach (no false positives) for the analysis of inefficiently-used containers. Second, we show that our approach can also be used for static profiling of programs which reasons about methods that are frequently invoked. Our experimental results show that our tool scales to relatively large benchmarks, and discovers relevant and useful information that can be used to optimize performance of the programs. },
author = {Chatterjee, Krishnendu and Pavlogiannis, Andreas and Velner, Yaron},
issn = {2664-1690},
pages = {33},
publisher = {IST Austria},
title = {{Quantitative interprocedural analysis}},
doi = {10.15479/AT:IST-2016-523-v1-1},
year = {2016},
}
@misc{5452,
author = {Pavlogiannis, Andreas and Tkadlec, Josef and Chatterjee, Krishnendu and Nowak, Martin},
issn = {2664-1690},
pages = {32},
publisher = {IST Austria},
title = {{Arbitrarily strong amplifiers of natural selection}},
doi = {10.15479/AT:IST-2017-728-v2-1},
year = {2016},
}
@misc{5446,
abstract = {We study the problem of developing efficient approaches for proving termination of recursive programs with one-dimensional arrays. Ranking functions serve as a sound and complete approach for proving termination of non-recursive programs without array operations. First, we generalize ranking functions to the notion of measure functions, and prove that measure functions (i) provide a sound method to prove termination of recursive programs (with one-dimensional arrays), and (ii) is both sound and complete over recursive programs without array operations. Our second contribution is the synthesis of measure functions of specific forms in polynomial time. More precisely, we prove that (i) polynomial measure functions over recursive programs can be synthesized in polynomial time through Farkas’ Lemma and Handelman’s Theorem, and (ii) measure functions involving logarithm and exponentiation can be synthesized in polynomial time through abstraction of logarithmic or exponential terms and Handelman’s Theorem. A key application of our method is the worst-case analysis of recursive programs. While previous methods obtain worst-case polynomial bounds of the form O(n^k), where k is an integer, our polynomial time methods can synthesize bounds of the form O(n log n), as well as O(n^x), where x is not an integer. We show the applicability of our automated technique to obtain worst-case complexity of classical recursive algorithms such as (i) Merge-Sort, the divideand-
conquer algorithm for the Closest-Pair problem, where we obtain O(n log n) worst-case bound, and (ii) Karatsuba’s algorithm for polynomial multiplication and Strassen’s algorithm for matrix multiplication, where we obtain O(n^x) bound, where x is not an integer and close to the best-known bounds for the respective algorithms. Finally, we present experimental results to demonstrate the
effectiveness of our approach.},
author = {Anonymous, 1 and Anonymous, 2 and Anonymous, 3},
issn = {2664-1690},
pages = {26},
publisher = {IST Austria},
title = {{Termination and worst-case analysis of recursive programs}},
year = {2016},
}
@misc{5453,
author = {Pavlogiannis, Andreas and Tkadlec, Josef and Chatterjee, Krishnendu and Nowak, Martin},
issn = {2664-1690},
pages = {34},
publisher = {IST Austria},
title = {{Arbitrarily strong amplifiers of natural selection}},
doi = {10.15479/AT:IST-2017-749-v3-1},
year = {2016},
}
@misc{5430,
abstract = {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 mul- tiplicative factor of ∊ in time O ( n · log( n/∊ )) 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 · log( | a · b · n | )) = O ( n · log( n · W )) , when the output is a b , as compared to the previously best known algorithm with running time O ( n 2 · log( n · W )) . Third, for the minimum initial credit problem we show that (i) for general graphs the problem can be solved in O ( n 2 · m ) time and the associated decision problem can be solved in O ( n · m ) time, improving the previous known O ( n 3 · m · log( n · W )) and O ( n 2 · m ) bounds, respectively; and (ii) for constant treewidth graphs we present an algorithm that requires O ( n · log n ) time, improving the previous known O ( n 4 · log( n · W )) bound. We have implemented some of our algorithms and show that they present a significant speedup on standard benchmarks.},
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Pavlogiannis, Andreas},
issn = {2664-1690},
pages = {31},
publisher = {IST Austria},
title = {{Faster algorithms for quantitative verification in constant treewidth graphs}},
doi = {10.15479/AT:IST-2015-319-v1-1},
year = {2015},
}
@misc{5435,
abstract = {We consider Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) objectives.
There have been two different views: (i) the expectation semantics, where the goal is to optimize the expected mean-payoff objective, and (ii) the satisfaction semantics, where the goal is to maximize the probability of runs such that the mean-payoff value stays above a given vector.
We consider the problem where the goal is to optimize the expectation under the constraint that the satisfaction semantics is ensured, and thus consider a generalization that unifies the existing semantics. Our problem captures the notion of optimization with respect to strategies that are risk-averse (i.e., ensures certain probabilistic guarantee).
Our main results are algorithms for the decision problem which are always polynomial in the size of the MDP.
We also show that an approximation of the Pareto-curve can be computed in time polynomial in the size of the MDP, and the approximation factor, but exponential in the number of dimensions. Finally, we present a complete characterization of the strategy complexity (in terms of memory bounds and randomization) required to solve our problem.},
author = {Chatterjee, Krishnendu and Komarkova, Zuzana and Kretinsky, Jan},
issn = {2664-1690},
pages = {51},
publisher = {IST Austria},
title = {{Unifying two views on multiple mean-payoff objectives in Markov decision processes}},
doi = {10.15479/AT:IST-2015-318-v2-1},
year = {2015},
}
@misc{5442,
abstract = {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.},
author = {Anonymous, 1 and Anonymous, 2 and Anonymous, 3 and Anonymous, 4},
issn = {2664-1690},
pages = {22},
publisher = {IST Austria},
title = {{Algorithms for algebraic path properties in concurrent systems of constant treewidth components}},
year = {2015},
}
@misc{5431,
abstract = {We consider finite-state concurrent stochastic games, played by k>=2 players for an infinite number of rounds, where in every round, each player simultaneously and independently of the other players chooses an action, whereafter the successor state is determined by a probability distribution given by the current state and the chosen actions. We consider reachability objectives that given a target set of states require that some state in the target set is visited, and the dual safety objectives that given a target set require that only states in the target set are visited. We are interested in the complexity of stationary strategies measured by their patience, which is defined as the inverse of the smallest non-zero probability employed.
Our main results are as follows: We show that in two-player zero-sum concurrent stochastic games (with reachability objective for one player and the complementary safety objective for the other player): (i) the optimal bound on the patience of optimal and epsilon-optimal strategies, for both players is doubly exponential; and (ii) even in games with a single non-absorbing state exponential (in the number of actions) patience is necessary. In general we study the class of non-zero-sum games admitting epsilon-Nash equilibria. We show that if there is at least one player with reachability objective, then doubly-exponential patience is needed in general for epsilon-Nash equilibrium strategies, whereas in contrast if all players have safety objectives, then the optimal bound on patience for epsilon-Nash equilibrium strategies is only exponential.},
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Hansen, Kristoffer},
issn = {2664-1690},
pages = {25},
publisher = {IST Austria},
title = {{The patience of concurrent stochastic games with safety and reachability objectives}},
doi = {10.15479/AT:IST-2015-322-v1-1},
year = {2015},
}
@misc{5443,
abstract = {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.},
author = {Chatterjee, Krishnendu and Chmelik, Martin and Davies, Jessica},
issn = {2664-1690},
pages = {23},
publisher = {IST Austria},
title = {{A symbolic SAT-based algorithm for almost-sure reachability with small strategies in POMDPs}},
doi = {10.15479/AT:IST-2015-325-v2-1},
year = {2015},
}
@misc{5429,
abstract = {We consider Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) objectives.
There have been two different views: (i) the expectation semantics, where the goal is to optimize the expected mean-payoff objective, and (ii) the satisfaction semantics, where the goal is to maximize the probability of runs such that the mean-payoff value stays above a given vector.
We consider the problem where the goal is to optimize the expectation under the constraint that the satisfaction semantics is ensured, and thus consider a generalization that unifies the existing semantics.
Our problem captures the notion of optimization with respect to strategies that are risk-averse (i.e., ensures certain probabilistic guarantee).
Our main results are algorithms for the decision problem which are always polynomial in the size of the MDP. We also show that an approximation of the Pareto-curve can be computed in time polynomial in the size of the MDP, and the approximation factor, but exponential in the number of dimensions.
Finally, we present a complete characterization of the strategy complexity (in terms of memory bounds and randomization) required to solve our problem.},
author = {Chatterjee, Krishnendu and Komarkova, Zuzana and Kretinsky, Jan},
issn = {2664-1690},
pages = {41},
publisher = {IST Austria},
title = {{Unifying two views on multiple mean-payoff objectives in Markov decision processes}},
doi = {10.15479/AT:IST-2015-318-v1-1},
year = {2015},
}
@misc{5436,
abstract = {Recently there has been a significant effort to handle 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, some basic system properties such as average response time cannot be expressed using weighted automata, nor in any other know decidable formalism. In this work, we introduce nested weighted automata as a natural extension of weighted automata which makes it possible to express important quantitative properties such as average response time.
In nested weighted automata, a master automaton spins off and collects results from weighted slave automata, each of which computes a quantity along a finite portion of an infinite word. Nested weighted automata can be viewed as the quantitative analogue of monitor automata, which are used in run-time verification. We establish an almost complete decidability picture for the basic decision problems about nested weighted automata, and illustrate their applicability in several domains. In particular, nested weighted automata can be used to decide average response time properties.},
author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Otop, Jan},
issn = {2664-1690},
pages = {29},
publisher = {IST Austria},
title = {{Nested weighted automata}},
doi = {10.15479/AT:IST-2015-170-v2-2},
year = {2015},
}
@misc{5444,
abstract = {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.},
author = {Reiter, Johannes and Makohon-Moore, Alvin and Gerold, Jeffrey and Bozic, Ivana and Chatterjee, Krishnendu and Iacobuzio-Donahue, Christine and Vogelstein, Bert and Nowak, Martin},
issn = {2664-1690},
pages = {25},
publisher = {IST Austria},
title = {{Reconstructing robust phylogenies of metastatic cancers}},
doi = {10.15479/AT:IST-2015-399-v1-1},
year = {2015},
}
@misc{5432,
abstract = {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 of the population. 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.
},
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Nowak, Martin},
issn = {2664-1690},
pages = {29},
publisher = {IST Austria},
title = {{The complexity of evolutionary games on graphs}},
doi = {10.15479/AT:IST-2015-323-v1-1},
year = {2015},
}
@misc{5437,
abstract = {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. },
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Pavlogiannis, Andreas},
issn = {2664-1690},
pages = {27},
publisher = {IST Austria},
title = {{Faster algorithms for quantitative verification in constant treewidth graphs}},
doi = {10.15479/AT:IST-2015-330-v2-1},
year = {2015},
}
@misc{5440,
abstract = {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.},
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Nowak, Martin},
issn = {2664-1690},
pages = {18},
publisher = {IST Austria},
title = {{The complexity of evolutionary games on graphs}},
doi = {10.15479/AT:IST-2015-323-v2-2},
year = {2015},
}
@misc{5438,
abstract = {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. },
author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Ibsen-Jensen, Rasmus and Otop, Jan},
issn = {2664-1690},
pages = {15},
publisher = {IST Austria},
title = {{Edit distance for pushdown automata}},
doi = {10.15479/AT:IST-2015-334-v1-1},
year = {2015},
}
@misc{5434,
abstract = {DEC-POMDPs extend POMDPs to a multi-agent setting, where several agents operate in an uncertain environment independently to achieve a joint objective. DEC-POMDPs have been studied with finite-horizon and infinite-horizon discounted-sum objectives, and there exist solvers both for exact and approximate solutions. In this work we consider Goal-DEC-POMDPs, where given a set of target states, the objective is to ensure that the target set is reached with minimal cost. We consider the indefinite-horizon (infinite-horizon with either discounted-sum, or undiscounted-sum, where absorbing goal states have zero-cost) problem. We present a new method to solve the problem that extends methods for finite-horizon DEC- POMDPs and the RTDP-Bel approach for POMDPs. We present experimental results on several examples, and show our approach presents promising results.},
author = {Anonymous, 1 and Anonymous, 2},
issn = {2664-1690},
pages = {16},
publisher = {IST Austria},
title = {{Optimal cost indefinite-horizon reachability in goal DEC-POMDPs}},
year = {2015},
}
@misc{5439,
abstract = {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. },
author = {Boker, Udi and Henzinger, Thomas A and Otop, Jan},
issn = {2664-1690},
pages = {20},
publisher = {IST Austria},
title = {{The target discounted-sum problem}},
doi = {10.15479/AT:IST-2015-335-v1-1},
year = {2015},
}
@misc{5441,
abstract = {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.},
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Goharshady, Amir and Pavlogiannis, Andreas},
issn = {2664-1690},
pages = {24},
publisher = {IST Austria},
title = {{Algorithms for algebraic path properties in concurrent systems of constant treewidth components}},
doi = {10.15479/AT:IST-2015-340-v1-1},
year = {2015},
}
@misc{5423,
abstract = {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. },
author = {Chatterjee, Krishnendu and Kössler, Alexander and Pavlogiannis, Andreas and Schmid, Ulrich},
issn = {2664-1690},
pages = {14},
publisher = {IST Austria},
title = {{A framework for automated competitive analysis of on-line scheduling of firm-deadline tasks}},
doi = {10.15479/AT:IST-2014-300-v1-1},
year = {2014},
}
@misc{5428,
abstract = {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.},
author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Otop, Jan and Velner, Yaron},
issn = {2664-1690},
pages = {26},
publisher = {IST Austria},
title = {{Quantitative fair simulation games}},
doi = {10.15479/AT:IST-2014-315-v1-1},
year = {2014},
}
@misc{5411,
abstract = {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.},
author = {Daca, Przemyslaw and Henzinger, Thomas A and Krenn, Willibald and Nickovic, Dejan},
issn = {2664-1690},
pages = {20},
publisher = {IST Austria},
title = {{Compositional specifications for IOCO testing}},
doi = {10.15479/AT:IST-2014-148-v2-1},
year = {2014},
}
@misc{5416,
abstract = {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.},
author = {Henzinger, Thomas A and Otop, Jan},
issn = {2664-1690},
pages = {22},
publisher = {IST Austria},
title = {{Model measuring for hybrid systems}},
doi = {10.15479/AT:IST-2014-171-v1-1},
year = {2014},
}
@misc{5417,
abstract = {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.},
author = {Henzinger, Thomas A and Otop, Jan},
issn = {2664-1690},
pages = {14},
publisher = {IST Austria},
title = {{From model checking to model measuring}},
doi = {10.15479/AT:IST-2014-172-v1-1},
year = {2014},
}
@misc{5424,
abstract = {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.},
author = {Chatterjee, Krishnendu and Chmelik, Martin and Gupta, Raghav and Kanodia, Ayush},
issn = {2664-1690},
pages = {12},
publisher = {IST Austria},
title = {{Qualitative analysis of POMDPs with temporal logic specifications for robotics applications}},
doi = {10.15479/AT:IST-2014-305-v1-1},
year = {2014},
}
@misc{5412,
abstract = {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. },
author = {Chatterjee, Krishnendu and Daca, Przemyslaw and Chmelik, Martin},
issn = {2664-1690},
pages = {31},
publisher = {IST Austria},
title = {{CEGAR for qualitative analysis of probabilistic systems}},
doi = {10.15479/AT:IST-2014-153-v1-1},
year = {2014},
}
@misc{5420,
abstract = {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).},
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus},
issn = {2664-1690},
pages = {49},
publisher = {IST Austria},
title = {{The value 1 problem for concurrent mean-payoff games}},
doi = {10.15479/AT:IST-2014-191-v1-1},
year = {2014},
}
@misc{5413,
abstract = {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. },
author = {Chatterjee, Krishnendu and Daca, Przemyslaw and Chmelik, Martin},
issn = {2664-1690},
pages = {33},
publisher = {IST Austria},
title = {{CEGAR for qualitative analysis of probabilistic systems}},
doi = {10.15479/AT:IST-2014-153-v2-2},
year = {2014},
}
@misc{5418,
abstract = {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.},
author = {Chatterjee, Krishnendu and Doyen, Laurent},
issn = {2664-1690},
pages = {18},
publisher = {IST Austria},
title = {{Games with a weak adversary}},
doi = {10.15479/AT:IST-2014-176-v1-1},
year = {2014},
}
@misc{5425,
abstract = { 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.},
author = {Anonymous, 1 and Anonymous, 2 and Anonymous, 3 and Anonymous, 4},
issn = {2664-1690},
pages = {22},
publisher = {IST Austria},
title = {{Optimal cost almost-sure reachability in POMDPs}},
year = {2014},
}
@misc{5419,
abstract = {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.},
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Pavlogiannis, Andreas},
issn = {2664-1690},
pages = {34},
publisher = {IST Austria},
title = {{Improved algorithms for reachability and shortest path on low tree-width graphs}},
doi = {10.15479/AT:IST-2014-187-v1-1},
year = {2014},
}
@misc{5421,
abstract = {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.},
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Nowak, Martin},
issn = {2664-1690},
pages = {27},
publisher = {IST Austria},
title = {{The complexity of evolution on graphs}},
doi = {10.15479/AT:IST-2014-190-v2-2},
year = {2014},
}
@misc{5426,
abstract = {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.},
author = {Chatterjee, Krishnendu and Chmelik, Martin and Gupta, Raghav and Kanodia, Ayush},
issn = {2664-1690},
pages = {10},
publisher = {IST Austria},
title = {{Qualitative analysis of POMDPs with temporal logic specifications for robotics applications}},
doi = {10.15479/AT:IST-2014-305-v2-1},
year = {2014},
}
@misc{5414,
abstract = {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. },
author = {Chatterjee, Krishnendu and Daca, Przemyslaw and Chmelik, Martin},
issn = {2664-1690},
pages = {33},
publisher = {IST Austria},
title = {{CEGAR for qualitative analysis of probabilistic systems}},
doi = {10.15479/AT:IST-2014-153-v3-1},
year = {2014},
}
@misc{5427,
abstract = {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.},
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Pavlogiannis, Andreas},
issn = {2664-1690},
pages = {24},
publisher = {IST Austria},
title = {{Optimal tree-decomposition balancing and reachability on low treewidth graphs}},
doi = {10.15479/AT:IST-2014-314-v1-1},
year = {2014},
}
@misc{5415,
abstract = {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. },
author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Otop, Jan},
issn = {2664-1690},
pages = {27},
publisher = {IST Austria},
title = {{Nested weighted automata}},
doi = {10.15479/AT:IST-2014-170-v1-1},
year = {2014},
}
@misc{5409,
abstract = {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.},
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Majumdar, Rupak},
issn = {2664-1690},
pages = {12},
publisher = {IST Austria},
title = {{Edit distance for timed automata}},
doi = {10.15479/AT:IST-2013-144-v1-1},
year = {2013},
}
@misc{6440,
abstract = {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.},
author = {Henzinger, Thomas A and Payer, Hannes and Sezgin, Ali},
issn = {2664-1690},
pages = {23},
publisher = {IST Austria},
title = {{Replacing competition with cooperation to achieve scalable lock-free FIFO queues }},
doi = {10.15479/AT:IST-2013-124-v1-1},
year = {2013},
}
@misc{5404,
abstract = {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.},
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus},
issn = {2664-1690},
pages = {29},
publisher = {IST Austria},
title = {{The complexity of ergodic games}},
doi = {10.15479/AT:IST-2013-127-v1-1},
year = {2013},
}
@misc{5405,
abstract = {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).},
author = {Chatterjee, Krishnendu and Doyen, Laurent and Gimbert, Hugo and Oualhadj, Youssouf},
issn = {2664-1690},
pages = {22},
publisher = {IST Austria},
title = {{Perfect-information stochastic mean-payoff parity games}},
doi = {10.15479/AT:IST-2013-128-v1-1},
year = {2013},
}
@misc{5400,
abstract = {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.},
author = {Chatterjee, Krishnendu and Chmelik, Martin and Tracol, Mathieu},
issn = {2664-1690},
pages = {41},
publisher = {IST Austria},
title = {{What is decidable about partially observable Markov decision processes with ω-regular objectives}},
doi = {10.15479/AT:IST-2013-109-v1-1},
year = {2013},
}
@misc{5406,
abstract = {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.},
author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Otop, Jan and Pavlogiannis, Andreas},
issn = {2664-1690},
pages = {11},
publisher = {IST Austria},
title = {{Distributed synthesis for LTL Fragments}},
doi = {10.15479/AT:IST-2013-130-v1-1},
year = {2013},
}