*-Continuous Kleene ω\omega-Algebras for Energy Problems

Energy problems are important in the formal analysis of embedded or autonomous systems. Using recent results on star-continuous Kleene omega-algebras, we show here that energy problems can be solved by algebraic manipulations on the transition matrix of energy automata. To this end, we prove general results about certain classes of finitely additive functions on complete lattices which should be of a more general interest.Comment: In Proceedings FICS 2015, arXiv:1509.0282

Undecidability of Two-dimensional Robot Games

Robot game is a two-player vector addition game played on the integer lattice $\mathbb{Z}^n$. Both players have sets of vectors and in each turn the vector chosen by a player is added to the current configuration vector of the game. One of the players, called Eve, tries to play the game from the initial configuration to the origin while the other player, Adam, tries to avoid the origin. The problem is to decide whether or not Eve has a winning strategy. In this paper we prove undecidability of the robot game in dimension two answering the question formulated by Doyen and Rabinovich in 2011 and closing the gap between undecidable and decidable cases

Kleene Algebras and Semimodules for Energy Problems

With the purpose of unifying a number of approaches to energy problems found in the literature, we introduce generalized energy automata. These are finite automata whose edges are labeled with energy functions that define how energy levels evolve during transitions. Uncovering a close connection between energy problems and reachability and B\"uchi acceptance for semiring-weighted automata, we show that these generalized energy problems are decidable. We also provide complexity results for important special cases

Optimal Strategy Synthesis for Request-Response Games

We show the existence and effective computability of optimal winning strategies for request-response games in case the quality of a play is measured by the limit superior of the mean accumulated waiting times between requests and their responses.Comment: The present paper is a revised version with simplified proofs of results announced in the conference paper of the same name presented at ATVA 2008, which in turn extended results of the third author's dissertatio

Verification for Timed Automata extended with Unbounded Discrete Data Structures

We study decidability of verification problems for timed automata extended with unbounded discrete data structures. More detailed, we extend timed automata with a pushdown stack. In this way, we obtain a strong model that may for instance be used to model real-time programs with procedure calls. It is long known that the reachability problem for this model is decidable. The goal of this paper is to identify subclasses of timed pushdown automata for which the language inclusion problem and related problems are decidable

Fixed-Dimensional Energy Games are in Pseudo-Polynomial Time

We generalise the hyperplane separation technique (Chatterjee and Velner, 2013) from multi-dimensional mean-payoff to energy games, and achieve an algorithm for solving the latter whose running time is exponential only in the dimension, but not in the number of vertices of the game graph. This answers an open question whether energy games with arbitrary initial credit can be solved in pseudo-polynomial time for fixed dimensions 3 or larger (Chaloupka, 2013). It also improves the complexity of solving multi-dimensional energy games with given initial credit from non-elementary (Br\'azdil, Jan\v{c}ar, and Ku\v{c}era, 2010) to 2EXPTIME, thus establishing their 2EXPTIME-completeness.Comment: Corrected proof of Lemma 6.2 (thanks to Dmitry Chistikov for spotting an error in the previous proof

Synthesis for multiobjective stochastic games: An application to autonomous urban driving

Abstract. We study strategy synthesis for stochastic two-player games with multiple objectives expressed as a conjunction of LTL and expected total reward goals. For stopping games, the strategies are constructed from the Pareto frontiers that we compute via value iteration. Since, in general, infinite memory is required for deterministic winning strategies in such games, our construction takes advantage of randomised memory updates in order to provide compact strategies. We implement our methods in PRISM-games, a model checker for stochastic multi-player games, and present a case study motivated by the DARPA Urban Challenge, illustrating how our methods can be used to synthesise strategies for high-level control of autonomous vehicles.