Jan Kretínský

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We study continuous-time stochastic games with time-bounded reachability objectives and time-abstract strategies. We show that each vertex in such a game has a value (i.e., an equilibrium probability), and we classify the conditions under which optimal strategies exist. Further, we show how to compute εoptimal strategies in finite games and provide detailed(More)
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(More)
We study the satisfiability problem for qualitative PCTL (probabilistic computation tree logic), which is obtained from "ordinary" CTL by replacing the EX, AX, EU, and AU operators with their qualitative counterparts X <sup>&gt;</sup> <sup>0</sup>, X <sup>=</sup> <sup>1</sup>, U <sup>&gt;</sup> <sup>0</sup>, and U <sup>=</sup> <sup>1</sup>, respectively. As(More)
Modal transition systems (MTS) is a formalism which extends the classical notion of labelled transition systems by introducing transitions of two types: must transitions that have to be present in any implementation of the MTS and may transitions that are allowed but not required. The MTS framework has proved to be useful as a specification formalism of(More)
We present a new algorithm to construct a deterministic Rabin automaton for an LTL formula φ. The automaton is the product of a master automaton and an array of slave automata, one for each Gsubformula of φ. The slave automaton for Gψ is in charge of recognizing whether FGψ holds. As opposed to standard determinization procedures, the states of all our(More)
Controller synthesis for general linear temporal logic (LTL) objectives is a challenging task. The standard approach involves translating the LTL objective into a deterministic parity automaton (DPA) by means of the Safra-Piterman construction. One of the challenges is the size of the DPA, which often grows very fast in practice, and can reach double(More)
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(More)