9 research outputs found
Visibly Pushdown Modular Games
Games on recursive game graphs can be used to reason about the control flow
of sequential programs with recursion. In games over recursive game graphs, the
most natural notion of strategy is the modular strategy, i.e., a strategy that
is local to a module and is oblivious to previous module invocations, and thus
does not depend on the context of invocation. In this work, we study for the
first time modular strategies with respect to winning conditions that can be
expressed by a pushdown automaton.
We show that such games are undecidable in general, and become decidable for
visibly pushdown automata specifications.
Our solution relies on a reduction to modular games with finite-state
automata winning conditions, which are known in the literature.
We carefully characterize the computational complexity of the considered
decision problem. In particular, we show that modular games with a universal
Buchi or co Buchi visibly pushdown winning condition are EXPTIME-complete, and
when the winning condition is given by a CARET or NWTL temporal logic formula
the problem is 2EXPTIME-complete, and it remains 2EXPTIME-hard even for simple
fragments of these logics.
As a further contribution, we present a different solution for modular games
with finite-state automata winning condition that runs faster than known
solutions for large specifications and many exits.Comment: In Proceedings GandALF 2014, arXiv:1408.556
無限ゲームと様相μ計算の部分体系についてのオートマトン理論的研究
要約のみTohoku University田中一之課
Borel Ranks and Wadge Degrees of Context Free Omega Languages
We show that, from a topological point of view, considering the Borel and the
Wadge hierarchies, 1-counter B\"uchi automata have the same accepting power
than Turing machines equipped with a B\"uchi acceptance condition. In
particular, for every non null recursive ordinal alpha, there exist some
Sigma^0_alpha-complete and some Pi^0_alpha-complete omega context free
languages accepted by 1-counter B\"uchi automata, and the supremum of the set
of Borel ranks of context free omega languages is the ordinal gamma^1_2 which
is strictly greater than the first non recursive ordinal. This very surprising
result gives answers to questions of H. Lescow and W. Thomas [Logical
Specifications of Infinite Computations, In:"A Decade of Concurrency", LNCS
803, Springer, 1994, p. 583-621]
Measuring Permissiveness in Parity Games: Mean-Payoff Parity Games Revisited
We study nondeterministic strategies in parity games with the aim of
computing a most permissive winning strategy. Following earlier work, we
measure permissiveness in terms of the average number/weight of transitions
blocked by the strategy. Using a translation into mean-payoff parity games, we
prove that the problem of computing (the permissiveness of) a most permissive
winning strategy is in NP intersected coNP. Along the way, we provide a new
study of mean-payoff parity games. In particular, we prove that the opponent
player has a memoryless optimal strategy and give a new algorithm for solving
these games.Comment: 30 pages, revised versio
Games with Winning Conditions of High Borel Complexity
International audienceWe first consider infinite two-player games on pushdown graphs. In previous work, Cachat, Duparc and Thomas [4] have presented a winning decidable condition that is Sigma_3-complete in the Borel hierarchy. This was the first example of a decidable winning condition of such Borel complexity. We extend this result by giving a family of decidable winning conditions of arbitrary finite Borel complexity. From this family, we deduce a family of decidable winning conditions of arbitrary finite Borel complexity for games played on finite graphs. The problem of deciding the winner for these conditions is shown to be non-elementary