Dominik Wojtczak

Recursive timed automata

We study recursive timed automata that extend timed automata with recursion. Timed automata, as introduced by Alur and Dill, are finite automata accompanied by a finite set of real-valued variables called clocks. Recursive timed automata are finite collections of timed automata extended with special states that correspond to (potentially recursive) invocations of other timed automata from their collection. During an invocation of a timed automaton, our model permits passing the values of clocks using both pass-byvalue and pass-by-reference mechanisms. We study the natural reachability and termination (reachability with empty invocation stack) problems for recursive timed automata. We show that these problems are decidable (in many cases with the same complexity as the reachability problem on timed automata) for recursive timed automata satisfying the following condition: during each invocation either all clocks are passed by reference or none is passed by reference. Furthermore, we show that for recursive timed automata that violate this condition reachability/termination problems are undecidable for automata with as few as three clocks. We also establish similar results for two-player game extension of our model against reachability/termination objective.

The Complexity of Nash Equilibria in Stochastic Multiplayer Games

textabstractWe analyse the computational complexity of finding Nash equilibria in stochastic multiplayer games with

PReMo: an analyzer for probabilistic recursive models

\omega

The complexity of nash equilibria in limit-average games

-regular objectives. We show that restricting the search space to equilibria whose payoffs fall into a certain interval may lead to undecidability. In particular, we prove that the following problem is undecidable: Given a game~

The Complexity of Nash Equilibria in Simple Stochastic Multiplayer Games

\mathcal{G}

Multi-objective Discounted Reward Verification in Graphs and MDPs

, does there exist a pure-strategy Nash equilibrium of~

An ordered approach to solving parity games in quasi polynomial time and quasi linear space

\mathcal{G}

Optimal scheduling for constant-rate multi-mode systems

where player 0 wins with probability~

Decision problems for Nash equilibria in stochastic games

1

Coordination Games on Directed Graphs

. Moreover, this problem remains undecidable if it is restricted to strategies with (unbounded) finite memory. However, if randomised strategies are allowed, decidability remains an open problem; we can only prove NP-hardness in this case. One way to obtain a provably decidable variant of the problem is to restrict the strategies to be positional or stationary. For the complexity of these two problems, we obtain a common lower bound of NP and upper bounds of NP and PSPACE respectively. Finally, we single out a special case of the general problem that, in many cases, admits an efficient solution. In particular, we prove that deciding the existence of an equilibrium in which each player either wins or loses with probability~