Vojtěch Řehák

Tomáš Brázdil, Jan Krčál, Jan Křetínský et al.

We study long run average behavior of generalized semi-Markov processes with both fixed-delay events as well as variable-delay events. We show that allowing two fixed-delay events and one variable-delay event may cause an unstable behavior of a GSMP. In particular, we show that a frequency of a given state may not be defined for almost all runs (or more generally, an invariant measure may not exist). We use this observation to disprove several results from literature. Next we study GSMP with at most one fixed-delay event combined with an arbitrary number of variable-delay events. We prove that such a GSMP always possesses an invariant measure which means that the frequencies of states are always well defined and we provide algorithms for approximation of these frequencies. Additionally, we show that the positive results remain valid even if we allow an arbitrary number of reasonably restricted fixed-delay events.

Tomáš Brázdil, Jan Krčál, Jan Křetínský et al.

We propose deterministic timed automata (DTA) as a model-independent language for specifying performance and dependability measures over continuous-time stochastic processes. Technically, these measures are defined as limit frequencies of locations (control states) of a DTA that observes computations of a given stochastic process. Then, we study the properties of DTA measures over semi-Markov processes in greater detail. We show that DTA measures over semi-Markov processes are well-defined with probability one, and there are only finitely many values that can be assumed by these measures with positive probability. We also give an algorithm which approximates these values and the associated probabilities up to an arbitrarily small given precision. Thus, we obtain a general and effective framework for analysing DTA measures over semi-Markov processes.

Martin Jonáš, Antonín Kučera, Vojtěch Kůr et al.

We introduce and study the multi-agent stochastic shortest path (MSSP) problem, in which $k$ agents strive to reach a target state, aiming to minimize the expected time to reach the target by any agent. We analyze the computational and strategy-complexity of the problem in both autonomous and coordinated settings, and we design efficient strategy-synthesis algorithms. The algorithms are experimentally evaluated on instances of increasing size against natural baselines.

Vojtěch Kůr, Vít Musil, Vojtěch Řehák

Adversarial Patrolling games form a subclass of Security games where a Defender moves between locations, guarding vulnerable targets. The main algorithmic problem is constructing a strategy for the Defender that minimizes the worst damage an Attacker can cause. We focus on the class of finite-memory (also known as regular) Defender's strategies that experimentally outperformed other competing classes. A finite-memory strategy can be seen as a positional strategy on a finite set of states. Each state consists of a pair of a location and a certain integer value--called memory. Existing algorithms improve the transitional probabilities between the states but require that the available memory size itself is assigned at each location manually. Choosing the right memory assignment is a well-known open and hard problem that hinders the usability of finite-memory strategies. We solve this issue by developing a general method that iteratively changes the memory assignment. Our algorithm can be used in connection with \emph{any} black-box strategy optimization tool. We evaluate our method on various experiments and show its robustness by solving instances of various patrolling models.

David Klaška, Antonín Kučera, Vojtěch Kůr et al.

The long-run average payoff per transition (mean payoff) is the main tool for specifying the performance and dependability properties of discrete systems. The problem of constructing a controller (strategy) simultaneously optimizing several mean payoffs has been deeply studied for stochastic and game-theoretic models. One common issue of the constructed controllers is the instability of the mean payoffs, measured by the deviations of the average rewards per transition computed in a finite "window" sliding along a run. Unfortunately, the problem of simultaneously optimizing the mean payoffs under local stability constraints is computationally hard, and the existing works do not provide a practically usable algorithm even for non-stochastic models such as two-player games. In this paper, we design and evaluate the first efficient and scalable solution to this problem applicable to Markov decision processes.

Tomáš Brázdil, Antonín Kučera, Vojtěch Řehák

We propose an algorithm for constructing efficient patrolling strategies in the Internet environment, where the protected targets are nodes connected to the network and the patrollers are software agents capable of detecting/preventing undesirable activities on the nodes. The algorithm is based on a novel compositional principle designed for a special class of strategies, and it can quickly construct (sub)optimal solutions even if the number of targets reaches hundreds of millions.