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Contribution à l'étude des jeux sur des graphes de processus à pile

Abstract : Two-player games on finite or infinite graphs are used to model several problems related to verification. The system is described by a game graph while the property to be checked is specified by a winning condition. The program is represented by the first player, Eve, and the environment is represented by the second player, Adam. In this framework, Eve has a winning strategy if and only if there exists a controller for the program that ensures that the given property is satisfied. The main problem is therefore to decide whether Eve has a winning strategy and to give it if exists.

In this thesis, we consider pushdown games that allow to describe natural infinite systems in a finite way. Classical winning conditions (reachability, Büchi or parity) and more specific conditions (as the one concerning the height of the stack) will be studied. We will also consider combinations of these ones.

A first contribution is a technique allowing to describe the winning positions (for several winning conditions) by alternating automata, inspired by work by Bouajjani, Esparza and Maler, and later by Cachat. In this thesis we generalize the technique to new winning conditions.

Another contribution is the description of a family of winning conditions of arbitrary finite Borel complexity for which games (on both finite and pushdown graphs) are decidable.

Using different techniques for games on subclasses of pushdown graphs (BPA graphs, and counter graphs) allows to improve the complexity bounds coming from the general case.

A last contribution is devoted to the pushdown games where the winning condition is either a boolean combination of a regular condition and a condition on the height of the stack, or a condition described by a visibly pushdown automaton. For both cases we provide optimal solutions.
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Contributor : Olivier Serre <>
Submitted on : Monday, January 9, 2006 - 3:20:21 PM
Last modification on : Saturday, March 28, 2020 - 2:16:45 AM
Long-term archiving on: : Saturday, April 3, 2010 - 9:00:36 PM



  • HAL Id : tel-00011326, version 1



Olivier Serre. Contribution à l'étude des jeux sur des graphes de processus à pile. Autre [cs.OH]. Université Paris VIII Vincennes-Saint Denis, 2004. Français. ⟨tel-00011326⟩



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