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

Memory Reduction via Delayed Simulation

We address a central (and classical) issue in the theory of infinite games: the reduction of the memory size that is needed to implement winning strategies in regular infinite games (i.e., controllers that ensure correct behavior against actions of the environment, when the specification is a regular omega-language). We propose an approach which attacks this problem before the construction of a strategy, by first reducing the game graph that is obtained from the specification. For the cases of specifications represented by "request-response"-requirements and general "fairness" conditions, we show that an exponential gain in the size of memory is possible.Comment: In Proceedings iWIGP 2011, arXiv:1102.374

Strategien in unendlichen Spielen mit Liveness-Gewinnbedingungen : Syntheseverfahren, Optimierung und Implementierung

In this thesis we develop methods for the solution of infinite games and present implementations of corresponding algorithms in the framework of a platform for the experimental study of automata theoretic algorithms. Our focus is on games with winning conditions that express certain liveness properties. A central type of liveness requirement in applications (e.g., in controller synthesis) is the “request-response condition”. It has the form of a conjunction of conditions “Whenever a “request”-state is visited, sometime later a corresponding “response”-state is visited”. A closely related winning condition is the “Streett condition” in which for repeated visits of certain states the repeated visits of other states is required. We present methods for the solution of request-response games and Streett games, the latter with an application in the analysis of live-sequence-charts. The main contribution is a quantitative analysis of request-response games. We pursue a natural approach for the quantitative evaluation of winning strategies by taking into account the waiting times that elapse between visits of “request”-states and subsequent visits of “response”-states in an infinite play. We introduce and discuss several related measures of plays in request-response games (over finite game arenas). For measures that induce a “penalty” which grows more than linearly in the waiting times, we present an algorithm to compute optimal winning strategies. The core of the argument is a reduction to mean-payoff games over finite arenas; it also shows that optimal strategies are implementable by finite-state machines. The experimental platform GaSt (”Games, Automata & Strategies”) offers numerous algorithms of the theory of omega-automata and for the solution of infinite games

Strategien in unendlichen Spielen mit Liveness-Gewinnbedingungen : Syntheseverfahren, Optimierung und Implementierung

In this thesis we develop methods for the solution of infinite games and present implementations of corresponding algorithms in the framework of a platform for the experimental study of automata theoretic algorithms. Our focus is on games with winning conditions that express certain liveness properties. A central type of liveness requirement in applications (e.g., in controller synthesis) is the “request-response condition”. It has the form of a conjunction of conditions “Whenever a “request”-state is visited, sometime later a corresponding “response”-state is visited”. A closely related winning condition is the “Streett condition” in which for repeated visits of certain states the repeated visits of other states is required. We present methods for the solution of request-response games and Streett games, the latter with an application in the analysis of live-sequence-charts. The main contribution is a quantitative analysis of request-response games. We pursue a natural approach for the quantitative evaluation of winning strategies by taking into account the waiting times that elapse between visits of “request”-states and subsequent visits of “response”-states in an infinite play. We introduce and discuss several related measures of plays in request-response games (over finite game arenas). For measures that induce a “penalty” which grows more than linearly in the waiting times, we present an algorithm to compute optimal winning strategies. The core of the argument is a reduction to mean-payoff games over finite arenas; it also shows that optimal strategies are implementable by finite-state machines. The experimental platform GaSt (”Games, Automata & Strategies”) offers numerous algorithms of the theory of omega-automata and for the solution of infinite games

Observations on Determinization of Büchi Automata

The two determinization procedures of Safra and Muller-Schupp for Büchi automata are compared, based on an implementation in a program called OmegaDet

Observations on determinization of Büchi Automata

The two determinization procedures of Safra and Muller-Schupp for Büchi automata are compared, based on an implementation in a program called OmegaDet

Symbolically Quantifying Response Time in Stochastic Models using Moments and Semirings

International audienceWe study quantitative properties of the response time in stochastic models. For instance, we are interested in quantifying bounds such that a high percentage of the runs answers a query within these bounds. To study such problems, computing probabilities on a state-space blown-up by a factor depending on the bound could be used, but this solution is not satisfactory when the bound is large. In this paper, we propose a new symbolic method to quantify bounds on the response time, using the moments of the distribution of simple stochastic systems. We prove that the distribution (and hence the bounds) is uniquely defined given its moments. We provide optimal bounds for the response time over all distributions having a pair of these moments. We explain how to symbolically compute in polynomial time any moment of the distribution of response times using adequately-defined semirings. This allows us to compute optimal bounds in parametric models and to reduce complexity for computing optimal bounds in hierarchical models