A game theoretical approach  to the algebraic counterpart  of the Wagner hierarchy : Part I

Jérémie Cabessa; Jacques Duparc

Displaying similar documents to “A game theoretical approach to the algebraic counterpart of the Wagner hierarchy : Part I”

A Game Theoretical Approach to The Algebraic Counterpart of The Wagner Hierarchy : Part II

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The algebraic counterpart of the Wagner hierarchy consists of a well-founded and decidable classification of finite pointed -semigroups of width and height . This paper completes the description of this algebraic hierarchy. We first give a purely algebraic decidability procedure of this partial ordering by introducing a graph representation of finite pointed -semigroups allowing to compute their precise Wagner degrees. The Wagner degree of any -rational language can therefore be computed...

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It is proposed to compare strategies in a parity game by comparing the sets of behaviours they allow. For such a game, there may be no winning strategy that encompasses all the behaviours of all winning strategies. It is shown, however, that there always exists a permissive strategy that encompasses all the behaviours of all memoryless strategies. An algorithm for finding such a permissive strategy is presented. Its complexity matches currently known upper bounds for the simpler problem...