A game theoretical approach to the algebraic counterpart of the Wagner hierarchy : Part I
Jérémie Cabessa, Jacques Duparc (2009)
RAIRO - Theoretical Informatics and Applications
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The algebraic study of formal languages shows that -rational sets correspond precisely to the -languages recognizable by finite -semigroups. Within this framework, we provide a construction of the algebraic counterpart of the Wagner hierarchy. We adopt a hierarchical game approach, by translating the Wadge theory from the -rational language to the -semigroup context. More precisely, we first show that the Wagner degree is indeed a syntactic invariant. We then define a reduction relation...