TY - CONF
AB - Graph games played by two players over finite-state graphs are central in many problems in computer science. In particular, graph games with ω -regular winning conditions, specified as parity objectives, which can express properties such as safety, liveness, fairness, are the basic framework for verification and synthesis of reactive systems. The decisions for a player at various states of the graph game are represented as strategies. While the algorithmic problem for solving graph games with parity objectives has been widely studied, the most prominent data-structure for strategy representation in graph games has been binary decision diagrams (BDDs). However, due to the bit-level representation, BDDs do not retain the inherent flavor of the decisions of strategies, and are notoriously hard to minimize to obtain succinct representation. In this work we propose decision trees for strategy representation in graph games. Decision trees retain the flavor of decisions of strategies and allow entropy-based minimization to obtain succinct trees. However, decision trees work in settings (e.g., probabilistic models) where errors are allowed, and overfitting of data is typically avoided. In contrast, for strategies in graph games no error is allowed, and the decision tree must represent the entire strategy. We develop new techniques to extend decision trees to overcome the above obstacles, while retaining the entropy-based techniques to obtain succinct trees. We have implemented our techniques to extend the existing decision tree solvers. We present experimental results for problems in reactive synthesis to show that decision trees provide a much more efficient data-structure for strategy representation as compared to BDDs.
AU - Brázdil, Tomáš
AU - Chatterjee, Krishnendu
AU - Kretinsky, Jan
AU - Toman, Viktor
ID - 297
TI - Strategy representation by decision trees in reactive synthesis
VL - 10805
ER -
TY - JOUR
AB - We consider Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) objectives. There exist 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 optimization with respect to both objectives at once, thus unifying the existing semantics. Precisely, the goal is to optimize the expectation while ensuring the satisfaction constraint. Our problem captures the notion of optimization with respect to strategies that are risk-averse (i.e., ensure certain probabilistic guarantee). Our main results are as follows: First, we present algorithms for the decision problems 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. Second, we present a complete characterization of the strategy complexity (in terms of memory bounds and randomization) required to solve our problem.
AU - Chatterjee, Krishnendu
AU - Křetínská, Zuzana
AU - Kretinsky, Jan
ID - 466
IS - 2
JF - Logical Methods in Computer Science
SN - 18605974
TI - Unifying two views on multiple mean-payoff objectives in Markov decision processes
VL - 13
ER -
TY - JOUR
AB - We present a new algorithm for the statistical model checking of Markov chains with respect to unbounded temporal properties, including full linear temporal logic. The main idea is that we monitor each simulation run on the fly, in order to detect quickly if a bottom strongly connected component is entered with high probability, in which case the simulation run can be terminated early. As a result, our simulation runs are often much shorter than required by termination bounds that are computed a priori for a desired level of confidence on a large state space. In comparison to previous algorithms for statistical model checking our method is not only faster in many cases but also requires less information about the system, namely, only the minimum transition probability that occurs in the Markov chain. In addition, our method can be generalised to unbounded quantitative properties such as mean-payoff bounds.
AU - Daca, Przemyslaw
AU - Henzinger, Thomas A
AU - Kretinsky, Jan
AU - Petrov, Tatjana
ID - 471
IS - 2
JF - ACM Transactions on Computational Logic (TOCL)
SN - 15293785
TI - Faster statistical model checking for unbounded temporal properties
VL - 18
ER -
TY - CONF
AB - Markov decision processes (MDPs) are standard models for probabilistic systems with non-deterministic behaviours. Long-run average rewards provide a mathematically elegant formalism for expressing long term performance. Value iteration (VI) is one of the simplest and most efficient algorithmic approaches to MDPs with other properties, such as reachability objectives. Unfortunately, a naive extension of VI does not work for MDPs with long-run average rewards, as there is no known stopping criterion. In this work our contributions are threefold. (1) We refute a conjecture related to stopping criteria for MDPs with long-run average rewards. (2) We present two practical algorithms for MDPs with long-run average rewards based on VI. First, we show that a combination of applying VI locally for each maximal end-component (MEC) and VI for reachability objectives can provide approximation guarantees. Second, extending the above approach with a simulation-guided on-demand variant of VI, we present an anytime algorithm that is able to deal with very large models. (3) Finally, we present experimental results showing that our methods significantly outperform the standard approaches on several benchmarks.
AU - Ashok, Pranav
AU - Chatterjee, Krishnendu
AU - Daca, Przemyslaw
AU - Kretinsky, Jan
AU - Meggendorfer, Tobias
ED - Majumdar, Rupak
ED - Kunčak, Viktor
ID - 645
SN - 978-331963386-2
TI - Value iteration for long run average reward in markov decision processes
VL - 10426
ER -
TY - JOUR
AB - We consider the problem of computing the set of initial states of a dynamical system such that there exists a control strategy to ensure that the trajectories satisfy a temporal logic specification with probability 1 (almost-surely). We focus on discrete-time, stochastic linear dynamics and specifications given as formulas of the Generalized Reactivity(1) fragment of Linear Temporal Logic over linear predicates in the states of the system. We propose a solution based on iterative abstraction-refinement, and turn-based 2-player probabilistic games. While the theoretical guarantee of our algorithm after any finite number of iterations is only a partial solution, we show that if our algorithm terminates, then the result is the set of all satisfying initial states. Moreover, for any (partial) solution our algorithm synthesizes witness control strategies to ensure almost-sure satisfaction of the temporal logic specification. While the proposed algorithm guarantees progress and soundness in every iteration, it is computationally demanding. We offer an alternative, more efficient solution for the reachability properties that decomposes the problem into a series of smaller problems of the same type. All algorithms are demonstrated on an illustrative case study.
AU - Svoreňová, Mária
AU - Kretinsky, Jan
AU - Chmelik, Martin
AU - Chatterjee, Krishnendu
AU - Cěrná, Ivana
AU - Belta, Cǎlin
ID - 1407
IS - 2
JF - Nonlinear Analysis: Hybrid Systems
TI - Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games
VL - 23
ER -
TY - CONF
AB - We introduce a general class of distances (metrics) between Markov chains, which are based on linear behaviour. This class encompasses distances given topologically (such as the total variation distance or trace distance) as well as by temporal logics or automata. We investigate which of the distances can be approximated by observing the systems, i.e. by black-box testing or simulation, and we provide both negative and positive results.
AU - Daca, Przemyslaw
AU - Henzinger, Thomas A
AU - Kretinsky, Jan
AU - Petrov, Tatjana
ID - 1093
TI - Linear distances between Markov chains
VL - 59
ER -
TY - CONF
AB - We present a new algorithm for the statistical model checking of Markov chains with respect to unbounded temporal properties, including full linear temporal logic. The main idea is that we monitor each simulation run on the fly, in order to detect quickly if a bottom strongly connected component is entered with high probability, in which case the simulation run can be terminated early. As a result, our simulation runs are often much shorter than required by termination bounds that are computed a priori for a desired level of confidence on a large state space. In comparison to previous algorithms for statistical model checking our method is not only faster in many cases but also requires less information about the system, namely, only the minimum transition probability that occurs in the Markov chain. In addition, our method can be generalised to unbounded quantitative properties such as mean-payoff bounds.
AU - Daca, Przemyslaw
AU - Henzinger, Thomas A
AU - Kretinsky, Jan
AU - Petrov, Tatjana
ID - 1234
TI - Faster statistical model checking for unbounded temporal properties
VL - 9636
ER -
TY - CONF
AB - We consider the problem of computing the set of initial states of a dynamical system such that there exists a control strategy to ensure that the trajectories satisfy a temporal logic specification with probability 1 (almost-surely). We focus on discrete-time, stochastic linear dynamics and specifications given as formulas of the Generalized Reactivity(1) fragment of Linear Temporal Logic over linear predicates in the states of the system. We propose a solution based on iterative abstraction-refinement, and turn-based 2-player probabilistic games. While the theoretical guarantee of our algorithm after any finite number of iterations is only a partial solution, we show that if our algorithm terminates, then the result is the set of satisfying initial states. Moreover, for any (partial) solution our algorithm synthesizes witness control strategies to ensure almost-sure satisfaction of the temporal logic specification. We demonstrate our approach on an illustrative case study.
AU - Svoreňová, Mária
AU - Kretinsky, Jan
AU - Chmelik, Martin
AU - Chatterjee, Krishnendu
AU - Cěrná, Ivana
AU - Belta, Cǎlin
ID - 1689
T2 - Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control
TI - Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games
ER -
TY - JOUR
AB - Modal transition systems (MTS) is a well-studied specification formalism of reactive systems supporting a step-wise refinement methodology. Despite its many advantages, the formalism as well as its currently known extensions are incapable of expressing some practically needed aspects in the refinement process like exclusive, conditional and persistent choices. We introduce a new model called parametric modal transition systems (PMTS) together with a general modal refinement notion that overcomes many of the limitations. We investigate the computational complexity of modal and thorough refinement checking on PMTS and its subclasses and provide a direct encoding of the modal refinement problem into quantified Boolean formulae, allowing us to employ state-of-the-art QBF solvers for modal refinement checking. The experiments we report on show that the feasibility of refinement checking is more influenced by the degree of nondeterminism rather than by the syntactic restrictions on the types of formulae allowed in the description of the PMTS.
AU - Beneš, Nikola
AU - Kretinsky, Jan
AU - Larsen, Kim
AU - Möller, Mikael
AU - Sickert, Salomon
AU - Srba, Jiří
ID - 1846
IS - 2-3
JF - Acta Informatica
TI - Refinement checking on parametric modal transition systems
VL - 52
ER -
TY - CONF
AB - We provide a framework for compositional and iterative design and verification of systems with quantitative information, such as rewards, time or energy. It is based on disjunctive modal transition systems where we allow actions to bear various types of quantitative information. Throughout the design process the actions can be further refined and the information made more precise. We show how to compute the results of standard operations on the systems, including the quotient (residual), which has not been previously considered for quantitative non-deterministic systems. Our quantitative framework has close connections to the modal nu-calculus and is compositional with respect to general notions of distances between systems and the standard operations.
AU - Fahrenberg, Uli
AU - Kretinsky, Jan
AU - Legay, Axel
AU - Traonouez, Louis
ID - 1882
TI - Compositionality for quantitative specifications
VL - 8997
ER -
TY - GEN
AB - 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.
AU - Chatterjee, Krishnendu
AU - Komarkova, Zuzana
AU - Kretinsky, Jan
ID - 5429
SN - 2664-1690
TI - Unifying two views on multiple mean-payoff objectives in Markov decision processes
ER -
TY - GEN
AB - 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.
AU - Chatterjee, Krishnendu
AU - Komarkova, Zuzana
AU - Kretinsky, Jan
ID - 5435
SN - 2664-1690
TI - Unifying two views on multiple mean-payoff objectives in Markov decision processes
ER -
TY - CONF
AB - We consider weighted automata with both positive and negative integer weights on edges and
study the problem of synchronization using adaptive strategies that may only observe whether
the current weight-level is negative or nonnegative. We show that the synchronization problem is decidable in polynomial time for deterministic weighted automata.
AU - Kretinsky, Jan
AU - Larsen, Kim
AU - Laursen, Simon
AU - Srba, Jiří
ID - 1499
TI - Polynomial time decidability of weighted synchronization under partial observability
VL - 42
ER -
TY - CONF
AB - We extend the theory of input-output conformance with operators for merge and quotient. The former is useful when testing against multiple requirements or views. The latter can be used to generate tests for patches of an already tested system. Both operators can combine systems with different action alphabets, which is usually the case when constructing complex systems and specifications from parts, for instance different views as well as newly defined functionality of a~previous version of the system.
AU - Beneš, Nikola
AU - Daca, Przemyslaw
AU - Henzinger, Thomas A
AU - Kretinsky, Jan
AU - Nickovic, Dejan
ID - 1502
SN - 978-1-4503-3471-6
TI - Complete composition operators for IOCO-testing theory
ER -
TY - CONF
AB - Quantitative extensions of temporal logics have recently attracted significant attention. In this work, we study frequency LTL (fLTL), an extension of LTL which allows to speak about frequencies of events along an execution. Such an extension is particularly useful for probabilistic systems that often cannot fulfil strict qualitative guarantees on the behaviour. It has been recently shown that controller synthesis for Markov decision processes and fLTL is decidable when all the bounds on frequencies are 1. As a step towards a complete quantitative solution, we show that the problem is decidable for the fragment fLTL\GU, where U does not occur in the scope of G (but still F can). Our solution is based on a novel translation of such quantitative formulae into equivalent deterministic automata.
AU - Forejt, Vojtěch
AU - Krčál, Jan
AU - Kretinsky, Jan
ID - 1594
TI - Controller synthesis for MDPs and frequency LTL\GU
VL - 9450
ER -
TY - CONF
AB - We propose a flexible exchange format for ω-automata, as typically used in formal verification, and implement support for it in a range of established tools. Our aim is to simplify the interaction of tools, helping the research community to build upon other people’s work. A key feature of the format is the use of very generic acceptance conditions, specified by Boolean combinations of acceptance primitives, rather than being limited to common cases such as Büchi, Streett, or Rabin. Such flexibility in the choice of acceptance conditions can be exploited in applications, for example in probabilistic model checking, and furthermore encourages the development of acceptance-agnostic tools for automata manipulations. The format allows acceptance conditions that are either state-based or transition-based, and also supports alternating automata.
AU - Babiak, Tomáš
AU - Blahoudek, František
AU - Duret Lutz, Alexandre
AU - Klein, Joachim
AU - Kretinsky, Jan
AU - Mueller, Daniel
AU - Parker, David
AU - Strejček, Jan
ID - 1601
TI - The Hanoi omega-automata format
VL - 9206
ER -
TY - CONF
AB - For deterministic systems, a counterexample to a property can simply be an error trace, whereas counterexamples in probabilistic systems are necessarily more complex. For instance, a set of erroneous traces with a sufficient cumulative probability mass can be used. Since these are too large objects to understand and manipulate, compact representations such as subchains have been considered. In the case of probabilistic systems with non-determinism, the situation is even more complex. While a subchain for a given strategy (or scheduler, resolving non-determinism) is a straightforward choice, we take a different approach. Instead, we focus on the strategy itself, and extract the most important decisions it makes, and present its succinct representation.
The key tools we employ to achieve this are (1) introducing a concept of importance of a state w.r.t. the strategy, and (2) learning using decision trees. There are three main consequent advantages of our approach. Firstly, it exploits the quantitative information on states, stressing the more important decisions. Secondly, it leads to a greater variability and degree of freedom in representing the strategies. Thirdly, the representation uses a self-explanatory data structure. In summary, our approach produces more succinct and more explainable strategies, as opposed to e.g. binary decision diagrams. Finally, our experimental results show that we can extract several rules describing the strategy even for very large systems that do not fit in memory, and based on the rules explain the erroneous behaviour.
AU - Brázdil, Tomáš
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Fellner, Andreas
AU - Kretinsky, Jan
ID - 1603
TI - Counterexample explanation by learning small strategies in Markov decision processes
VL - 9206
ER -
TY - CONF
AB - We consider Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) objectives. There exist 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 optimization with respect to both objectives at once, thus unifying the existing semantics. Precisely, the goal is to optimize the expectation while ensuring the satisfaction constraint. Our problem captures the notion of optimization with respect to strategies that are risk-averse (i.e., Ensure certain probabilistic guarantee). Our main results are as follows: First, we present algorithms for the decision problems, 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. Second, we present a complete characterization of the strategy complexity (in terms of memory bounds and randomization) required to solve our problem.
AU - Chatterjee, Krishnendu
AU - Komárková, Zuzana
AU - Kretinsky, Jan
ID - 1657
TI - Unifying two views on multiple mean-payoff objectives in Markov decision processes
ER -
TY - CONF
AB - We present a tool for translating LTL formulae into deterministic ω-automata. It is the first tool that covers the whole LTL that does not use Safra’s determinization or any of its variants. This leads to smaller automata. There are several outputs of the tool: firstly, deterministic Rabin automata, which are the standard input for probabilistic model checking, e.g. for the probabilistic model-checker PRISM; secondly, deterministic generalized Rabin automata, which can also be used for probabilistic model checking and are sometimes by orders of magnitude smaller. We also link our tool to PRISM and show that this leads to a significant speed-up of probabilistic LTL model checking, especially with the generalized Rabin automata.
AU - Komárková, Zuzana
AU - Kretinsky, Jan
ED - Cassez, Franck
ED - Raskin, Jean-François
ID - 2026
T2 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
TI - Rabinizer 3: Safraless translation of ltl to small deterministic automata
VL - 8837
ER -
TY - CONF
AB - We present a general framework for applying machine-learning algorithms to the verification of Markov decision processes (MDPs). The primary goal of these techniques is to improve performance by avoiding an exhaustive exploration of the state space. Our framework focuses on probabilistic reachability, which is a core property for verification, and is illustrated through two distinct instantiations. The first assumes that full knowledge of the MDP is available, and performs a heuristic-driven partial exploration of the model, yielding precise lower and upper bounds on the required probability. The second tackles the case where we may only sample the MDP, and yields probabilistic guarantees, again in terms of both the lower and upper bounds, which provides efficient stopping criteria for the approximation. The latter is the first extension of statistical model checking for unbounded properties inMDPs. In contrast with other related techniques, our approach is not restricted to time-bounded (finite-horizon) or discounted properties, nor does it assume any particular properties of the MDP. We also show how our methods extend to LTL objectives. We present experimental results showing the performance of our framework on several examples.
AU - Brázdil, Tomáš
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Forejt, Vojtěch
AU - Kretinsky, Jan
AU - Kwiatkowska, Marta
AU - Parker, David
AU - Ujma, Mateusz
ED - Cassez, Franck
ED - Raskin, Jean-François
ID - 2027
T2 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
TI - Verification of markov decision processes using learning algorithms
VL - 8837
ER -