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Vojtech Forejt

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4 papers

2 author rows

LPAR Conference 2015 Conference Paper

Controller Synthesis for MDPs and Frequency LTL \GU

Vojtech Forejt
Jan Krcál
Jan Kretínský

Abstract 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 ${{\text {fLTL}_{\setminus \mathbf{G}\mathbf U}}}$, where $\mathbf U$ does not occur in the scope of $\mathbf{G}$ (but still $\mathbf{F}$ can). Our solution is based on a novel translation of such quantitative formulae into equivalent deterministic automata.

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Highlights Conference 2015 Conference Abstract

On Frequency LTL in Probabilistic Systems

Vojtech Forejt

We study frequency linear-time temporal logic (fLTL) which extends the linear-time temporal logic (LTL) with a path operator $\Gf{p}$ expressing that on a path, certain formula holds with at least a given frequency $p$, thus relaxing the semantics of the usual $\mathbf{G}$ operator of LTL. Such logic is particularly useful in probabilistic systems, where some undesirable events such as random failures may occur and are acceptable if they are rare enough. Frequency-related extensions of LTL have been previously studied by several authors, where mostly the logic is equipped with an extended ``until'' and ``globally'' operator, leading to undecidability of most interesting problems. For the variant we study, we are able to establish fundamental decidability results. We show that for Markov chains, the problem of computing the probability with which a given fLTL formula holds has the same complexity as the analogous problem for LTL. We also show that for Markov decision processes the problem becomes more delicate, but when restricting the frequency bound $p$ to be 1 and negations not to be outside any $\mathbf{G}^p$ operator, we can compute the maximum probability of satisfying the fLTL formula. This can be again performed with the same time complexity as for the ordinary LTL formulas.

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LPAR Conference 2013 Conference Paper

Multi-objective Discounted Reward Verification in Graphs and MDPs

Krishnendu Chatterjee
Vojtech Forejt
Dominik Wojtczak

Abstract We study the problem of achieving a given value in Markov decision processes (MDPs) with several independent discounted reward objectives. We consider a generalised version of discounted reward objectives, in which the amount of discounting depends on the states visited and on the objective. This definition extends the usual definition of discounted reward, and allows to capture the systems in which the value of different commodities diminish at different and variable rates. We establish results for two prominent subclasses of the problem, namely state-discount models where the discount factors are only dependent on the state of the MDP (and independent of the objective), and reward-discount models where they are only dependent on the objective (but not on the state of the MDP). For the state-discount models we use a straightforward reduction to expected total reward and show that the problem whether a value is achievable can be solved in polynomial time. For the reward-discount model we show that memory and randomisation of the strategies are required, but nevertheless that the problem is decidable and it is sufficient to consider strategies which after a certain number of steps behave in a memoryless way. For the general case, we show that when restricted to graphs (i. e. MDPs with no randomisation), pure strategies and discount factors of the form 1/ n where n is an integer, the problem is in PSPACE and finite memory suffices for achieving a given value. We also show that when the discount factors are not of the form 1/ n, the memory required by a strategy can be infinite.

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MFCS Conference 2013 Conference Paper

On Stochastic Games with Multiple Objectives

Taolue Chen 0001
Vojtech Forejt
Marta Kwiatkowska
Aistis Simaitis
Clemens Wiltsche

Abstract We study two-player stochastic games, where the goal of one player is to satisfy a formula given as a positive boolean combination of expected total reward objectives and the behaviour of the second player is adversarial. Such games are important for modelling, synthesis and verification of open systems with stochastic behaviour. We show that finding a winning strategy is PSPACE-hard in general and undecidable for deterministic strategies. We also prove that optimal strategies, if they exists, may require infinite memory and randomisation. However, when restricted to disjunctions of objectives only, memoryless deterministic strategies suffice, and the problem of deciding whether a winning strategy exists is NP-complete. We also present algorithms to approximate the Pareto sets of achievable objectives for the class of stopping games.

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