TY - CONF
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 - 3345
TI - Energy and mean-payoff parity Markov Decision Processes
VL - 6907
ER -
TY - CONF
AB - We study Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) functions. We consider two different objectives, namely, expectation and satisfaction objectives. Given an MDP with k reward functions, in the expectation objective the goal is to maximize the expected limit-average value, and in the satisfaction objective the goal is to maximize the probability of runs such that the limit-average value stays above a given vector. We show that under the expectation objective, in contrast to the single-objective case, both randomization and memory are necessary for strategies, and that finite-memory randomized strategies are sufficient. Under the satisfaction objective, in contrast to the single-objective case, infinite memory is necessary for strategies, and that randomized memoryless strategies are sufficient for epsilon-approximation, for all epsilon>;0. We further prove that the decision problems for both expectation and satisfaction objectives can be solved in polynomial time and the trade-off curve (Pareto curve) can be epsilon-approximated in time polynomial in the size of the MDP and 1/epsilon, and exponential in the number of reward functions, for all epsilon>;0. Our results also reveal flaws in previous work for MDPs with multiple mean-payoff functions under the expectation objective, correct the flaws and obtain improved results.
AU - Brázdil, Tomáš
AU - Brožek, Václav
AU - Chatterjee, Krishnendu
AU - Forejt, Vojtěch
AU - Kučera, Antonín
ID - 3346
TI - Two views on multiple mean payoff objectives in Markov Decision Processes
ER -
TY - CONF
AB - The class of omega-regular languages provides a robust specification language in verification. Every omega-regular condition can be decomposed into a safety part and a liveness part. The liveness part ensures that something good happens "eventually". Finitary liveness was proposed by Alur and Henzinger as a stronger formulation of liveness. It requires that there exists an unknown, fixed bound b such that something good happens within b transitions. In this work we consider automata with finitary acceptance conditions defined by finitary Buchi, parity and Streett languages. We study languages expressible by such automata: we give their topological complexity and present a regular-expression characterization. We compare the expressive power of finitary automata and give optimal algorithms for classical decisions questions. We show that the finitary languages are Sigma 2-complete; we present a complete picture of the expressive power of various classes of automata with finitary and infinitary acceptance conditions; we show that the languages defined by finitary parity automata exactly characterize the star-free fragment of omega B-regular languages; and we show that emptiness is NLOGSPACE-complete and universality as well as language inclusion are PSPACE-complete for finitary parity and Streett automata.
AU - Chatterjee, Krishnendu
AU - Fijalkow, Nathanaël
ID - 3347
TI - Finitary languages
VL - 6638
ER -
TY - CONF
AB - We study synthesis of controllers for real-time systems, where the objective is to stay in a given safe set. The problem is solved by obtaining winning strategies in the setting of concurrent two-player timed automaton games with safety objectives. To prevent a player from winning by blocking time, we restrict each player to strategies that ensure that the player cannot be responsible for causing a zeno run. We construct winning strategies for the controller which require access only to (1) the system clocks (thus, controllers which require their own internal infinitely precise clocks are not necessary), and (2) a linear (in the number of clocks) number of memory bits. Precisely, we show that for safety objectives, a memory of size (3 · |C|+lg(|C|+1)) bits suffices for winning controller strategies, where C is the set of clocks of the timed automaton game, significantly improving the previous known exponential bound. We also settle the open question of whether winning region controller strategies require memory for safety objectives by showing with an example the necessity of memory for region strategies to win for safety objectives.
AU - Chatterjee, Krishnendu
AU - Prabhu, Vinayak
ID - 3348
TI - Synthesis of memory efficient real time controllers for safety objectives
ER -
TY - CONF
AB - Games on graphs provide a natural model for reactive non-terminating systems. In such games, the interaction of two players on an arena results in an infinite path that describes a run of the system. Different settings are used to model various open systems in computer science, as for instance turn-based or concurrent moves, and deterministic or stochastic transitions. In this paper, we are interested in turn-based games, and specifically in deterministic parity games and stochastic reachability games (also known as simple stochastic games). We present a simple, direct and efficient reduction from deterministic parity games to simple stochastic games: it yields an arena whose size is linear up to a logarithmic factor in size of the original arena.
AU - Chatterjee, Krishnendu
AU - Fijalkow, Nathanaël
ID - 3349
TI - A reduction from parity games to simple stochastic games
VL - 54
ER -
TY - CONF
AB - In two-player games on graph, the players construct an infinite path through the game graph and get a reward computed by a payoff function over infinite paths. Over weighted graphs, the typical and most studied payoff functions compute the limit-average or the discounted sum of the rewards along the path. Besides their simple definition, these two payoff functions enjoy the property that memoryless optimal strategies always exist. In an attempt to construct other simple payoff functions, we define a class of payoff functions which compute an (infinite) weighted average of the rewards. This new class contains both the limit-average and the discounted sum functions, and we show that they are the only members of this class which induce memoryless optimal strategies, showing that there is essentially no other simple payoff functions.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Singh, Rohit
ED - Owe, Olaf
ED - Steffen, Martin
ED - Telle, Jan Arne
ID - 3351
TI - On memoryless quantitative objectives
VL - 6914
ER -
TY - JOUR
AB - Compositional theories are crucial when designing large and complex systems from smaller components. In this work we propose such a theory for synchronous concurrent systems. Our approach follows so-called interface theories, which use game-theoretic interpretations of composition and refinement. These are appropriate for systems with distinct inputs and outputs, and explicit conditions on inputs that must be enforced during composition. Our interfaces model systems that execute in an infinite sequence of synchronous rounds. At each round, a contract must be satisfied. The contract is simply a relation specifying the set of valid input/output pairs. Interfaces can be composed by parallel, serial or feedback composition. A refinement relation between interfaces is defined, and shown to have two main properties: (1) it is preserved by composition, and (2) it is equivalent to substitutability, namely, the ability to replace an interface by another one in any context. Shared refinement and abstraction operators, corresponding to greatest lower and least upper bounds with respect to refinement, are also defined. Input-complete interfaces, that impose no restrictions on inputs, and deterministic interfaces, that produce a unique output for any legal input, are discussed as special cases, and an interesting duality between the two classes is exposed. A number of illustrative examples are provided, as well as algorithms to compute compositions, check refinement, and so on, for finite-state interfaces.
AU - Tripakis, Stavros
AU - Lickly, Ben
AU - Henzinger, Thomas A
AU - Lee, Edward
ID - 3353
IS - 4
JF - ACM Transactions on Programming Languages and Systems (TOPLAS)
TI - A theory of synchronous relational interfaces
VL - 33
ER -
TY - CONF
AB - Byzantine Fault Tolerant (BFT) protocols aim to improve the reliability of distributed systems. They enable systems to tolerate arbitrary failures in a bounded number of nodes. BFT protocols are usually proven correct for certain safety and liveness properties. However, recent studies have shown that the performance of state-of-the-art BFT protocols decreases drastically in the presence of even a single malicious node. This motivates a formal quantitative analysis of BFT protocols to investigate their performance characteristics under different scenarios. We present HyPerf, a new hybrid methodology based on model checking and simulation techniques for evaluating the performance of BFT protocols. We build a transition system corresponding to a BFT protocol and systematically explore the set of behaviors allowed by the protocol. We associate certain timing information with different operations in the protocol, like cryptographic operations and message transmission. After an elaborate state exploration, we use the time information to evaluate the performance characteristics of the protocol using simulation techniques. We integrate our framework in Mace, a tool for building and verifying distributed systems. We evaluate the performance of PBFT using our framework. We describe two different use-cases of our methodology. For the benign operation of the protocol, we use the time information as random variables to compute the probability distribution of the execution times. In the presence of faults, we estimate the worst-case performance of the protocol for various attacks that can be employed by malicious nodes. Our results show the importance of hybrid techniques in systematically analyzing the performance of large-scale systems.
AU - Halalai, Raluca
AU - Henzinger, Thomas A
AU - Singh, Vasu
ID - 3355
TI - Quantitative evaluation of BFT protocols
ER -
TY - CONF
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 - 3356
TI - Temporal specifications with accumulative values
ER -
TY - CONF
AB - The static scheduling problem often arises as a fundamental problem in real-time systems and grid computing. We consider the problem of statically scheduling a large job expressed as a task graph on a large number of computing nodes, such as a data center. This paper solves the large-scale static scheduling problem using abstraction refinement, a technique commonly used in formal verification to efficiently solve computationally hard problems. A scheduler based on abstraction refinement first attempts to solve the scheduling problem with abstract representations of the job and the computing resources. As abstract representations are generally small, the scheduling can be done reasonably fast. If the obtained schedule does not meet specified quality conditions (like data center utilization or schedule makespan) then the scheduler refines the job and data center abstractions and, again solves the scheduling problem. We develop different schedulers based on abstraction refinement. We implemented these schedulers and used them to schedule task graphs from various computing domains on simulated data centers with realistic topologies. We compared the speed of scheduling and the quality of the produced schedules with our abstraction refinement schedulers against a baseline scheduler that does not use any abstraction. We conclude that abstraction refinement techniques give a significant speed-up compared to traditional static scheduling heuristics, at a reasonable cost in the quality of the produced schedules. We further used our static schedulers in an actual system that we deployed on Amazon EC2 and compared it against the Hadoop dynamic scheduler for large MapReduce jobs. Our experiments indicate that there is great potential for static scheduling techniques.
AU - Henzinger, Thomas A
AU - Singh, Vasu
AU - Wies, Thomas
AU - Zufferey, Damien
ID - 3358
TI - Scheduling large jobs by abstraction refinement
ER -
TY - CONF
AB - A discounted-sum automaton (NDA) is a nondeterministic finite automaton with edge weights, which values a run by the discounted sum of visited edge weights. More precisely, the weight in the i-th position of the run is divided by lambda^i, where the discount factor lambda is a fixed rational number greater than 1. Discounted summation is a common and useful measuring scheme, especially for infinite sequences, which reflects the assumption that earlier weights are more important than later weights. Determinizing automata is often essential, for example, in formal verification, where there are polynomial algorithms for comparing two deterministic NDAs, while the equivalence problem for NDAs is not known to be decidable. Unfortunately, however, discounted-sum automata are, in general, not determinizable: it is currently known that for every rational discount factor 1 < lambda < 2, there is an NDA with lambda (denoted lambda-NDA) that cannot be determinized. We provide positive news, showing that every NDA with an integral factor is determinizable. We also complete the picture by proving that the integers characterize exactly the discount factors that guarantee determinizability: we show that for every non-integral rational factor lambda, there is a nondeterminizable lambda-NDA. Finally, we prove that the class of NDAs with integral discount factors enjoys closure under the algebraic operations min, max, addition, and subtraction, which is not the case for general NDAs nor for deterministic NDAs. This shows that for integral discount factors, the class of NDAs forms an attractive specification formalism in quantitative formal verification. All our results hold equally for automata over finite words and for automata over infinite words.
AU - Boker, Udi
AU - Henzinger, Thomas A
ID - 3360
TI - Determinizing discounted-sum automata
VL - 12
ER -
TY - CONF
AB - In this paper, we investigate the computational complexity of quantitative information flow (QIF) problems. Information-theoretic quantitative relaxations of noninterference (based on Shannon entropy)have been introduced to enable more fine-grained reasoning about programs in situations where limited information flow is acceptable. The QIF bounding problem asks whether the information flow in a given program is bounded by a constant $d$. Our first result is that the QIF bounding problem is PSPACE-complete. The QIF memoryless synthesis problem asks whether it is possible to resolve nondeterministic choices in a given partial program in such a way that in the resulting deterministic program, the quantitative information flow is bounded by a given constant $d$. Our second result is that the QIF memoryless synthesis problem is also EXPTIME-complete. The QIF memoryless synthesis problem generalizes to QIF general synthesis problem which does not impose the memoryless requirement (that is, by allowing the synthesized program to have more variables then the original partial program). Our third result is that the QIF general synthesis problem is EXPTIME-hard.
AU - Cerny, Pavol
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
ID - 3361
TI - The complexity of quantitative information flow problems
ER -
TY - CONF
AB - State-transition systems communicating by shared variables have been the underlying model of choice for applications of model checking. Such formalisms, however, have difficulty with modeling process creation or death and communication reconfigurability. Here, we introduce “dynamic reactive modules” (DRM), a state-transition modeling formalism that supports dynamic reconfiguration and creation/death of processes. The resulting formalism supports two types of variables, data variables and reference variables. Reference variables enable changing the connectivity between processes and referring to instances of processes. We show how this new formalism supports parallel composition and refinement through trace containment. DRM provide a natural language for modeling (and ultimately reasoning about) biological systems and multiple threads communicating through shared variables.
AU - Fisher, Jasmin
AU - Henzinger, Thomas A
AU - Nickovic, Dejan
AU - Piterman, Nir
AU - Singh, Anmol
AU - Vardi, Moshe
ID - 3362
TI - Dynamic reactive modules
VL - 6901
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 for probabilistic finite automata and present a complete characterization of the decidability and undecidability frontier of the quantitative and qualitative decision problems for probabilistic automata on infinite words.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Tracol, Mathieu
ID - 3363
TI - The decidability frontier for probabilistic automata on infinite words
ER -
TY - JOUR
AB - Molecular noise, which arises from the randomness of the discrete events in the cell, significantly influences fundamental biological processes. Discrete-state continuous-time stochastic models (CTMC) can be used to describe such effects, but the calculation of the probabilities of certain events is computationally expensive. We present a comparison of two analysis approaches for CTMC. On one hand, we estimate the probabilities of interest using repeated Gillespie simulation and determine the statistical accuracy that we obtain. On the other hand, we apply a numerical reachability analysis that approximates the probability distributions of the system at several time instances. We use examples of cellular processes to demonstrate the superiority of the reachability analysis if accurate results are required.
AU - Didier, Frédéric
AU - Henzinger, Thomas A
AU - Mateescu, Maria
AU - Wolf, Verena
ID - 3364
IS - 21
JF - Theoretical Computer Science
TI - Approximation of event probabilities in noisy cellular processes
VL - 412
ER -
TY - CONF
AB - We present the tool Quasy, a quantitative synthesis tool. Quasy takes qualitative and quantitative specifications and automatically constructs a system that satisfies the qualitative specification and optimizes the quantitative specification, if such a system exists. The user can choose between a system that satisfies and optimizes the specifications (a) under all possible environment behaviors or (b) under the most-likely environment behaviors given as a probability distribution on the possible input sequences. Quasy solves these two quantitative synthesis problems by reduction to instances of 2-player games and Markov Decision Processes (MDPs) with quantitative winning objectives. Quasy can also be seen as a game solver for quantitative games. Most notable, it can solve lexicographic mean-payoff games with 2 players, MDPs with mean-payoff objectives, and ergodic MDPs with mean-payoff parity objectives.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Jobstmann, Barbara
AU - Singh, Rohit
ID - 3365
TI - QUASY: quantitative synthesis tool
VL - 6605
ER -
TY - CONF
AB - We present an algorithmic method for the quantitative, performance-aware synthesis of concurrent programs. The input consists of a nondeterministic partial program and of a parametric performance model. The nondeterminism allows the programmer to omit which (if any) synchronization construct is used at a particular program location. The performance model, specified as a weighted automaton, can capture system architectures by assigning different costs to actions such as locking, context switching, and memory and cache accesses. The quantitative synthesis problem is to automatically resolve the nondeterminism of the partial program so that both correctness is guaranteed and performance is optimal. As is standard for shared memory concurrency, correctness is formalized "specification free", in particular as race freedom or deadlock freedom. For worst-case (average-case) performance, we show that the problem can be reduced to 2-player graph games (with probabilistic transitions) with quantitative objectives. While we show, using game-theoretic methods, that the synthesis problem is Nexp-complete, we present an algorithmic method and an implementation that works efficiently for concurrent programs and performance models of practical interest. We have implemented a prototype tool and used it to synthesize finite-state concurrent programs that exhibit different programming patterns, for several performance models representing different architectures.
AU - Cerny, Pavol
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Radhakrishna, Arjun
AU - Singh, Rohit
ED - Gopalakrishnan, Ganesh
ED - Qadeer, Shaz
ID - 3366
TI - Quantitative synthesis for concurrent programs
VL - 6806
ER -
TY - JOUR
AB - Tissue surface tension (TST) is an important mechanical property influencing cell sorting and tissue envelopment. The study by Manning et al. (1) reported on a mathematical model describing TST on the basis of the balance between adhesive and tensile properties of the constituent cells. The model predicts that, in high-adhesion cell aggregates, surface cells will be stretched to maintain the same area of cell–cell contact as interior bulk cells, resulting in an elongated and flattened cell shape. The authors (1) observed flat and elongated cells at the surface of high-adhesion zebrafish germ-layer explants, which they argue are undifferentiated stretched germ-layer progenitor cells, and they use this observation as a validation of their model.
AU - Krens, Gabriel
AU - Möllmert, Stephanie
AU - Heisenberg, Carl-Philipp J
ID - 3368
IS - 3
JF - PNAS
TI - Enveloping cell layer differentiation at the surface of zebrafish germ layer tissue explants
VL - 108
ER -
TY - JOUR
AB - Supertree methods are widely applied and give rise to new conclusions about phylogenies (e.g., Bininda-Emonds et al. 2007). Although several desiderata for supertree methods exist (Wilkinson, Thorley, et al. 2004), only few of them have been studied in greater detail, examples include shape bias (Wilkinson et al. 2005) or pareto properties (Wilkinson et al. 2007). Here I look more closely at two matrix representation methods, matrix representation with compatibility (MRC) and matrix representation with parsimony (MRP). Different null models of random data are studied and the resulting tree shapes are investigated. Thereby I consider unrooted trees and a bias in tree shape is determined by a tree balance measure. The measure for unrooted trees is a modification of a tree balance measure for rooted trees. I observe that depending on the underlying null model of random data, the methods may resolve conflict in favor of more balanced tree shapes. The analyses refer only to trees with the same taxon set, also known as the consensus setting (e.g., Wilkinson et al. 2007), but I will be able to draw conclusions on how to deal with missing data.
AU - Kupczok, Anne
ID - 3370
IS - 2
JF - Systematic Biology
TI - Consequences of different null models on the tree shape bias of supertree methods
VL - 60
ER -
TY - JOUR
AB - The Minisymposium “Cell Migration and Motility” was attended by approximately 500 visitors and covered a broad range of questions in the field using diverse model systems. Topics comprised actin dynamics, cell polarity, force transduction, signal transduction, bar- rier transmigration, and chemotactic guidance.
AU - Sixt, Michael K
AU - Parent, Carole
ID - 3371
IS - 6
JF - Molecular Biology and Evolution
TI - Cells on the move in Philadelphia
VL - 22
ER -