The Algebraic Counterpart of the Wagner Hierarchy
نویسندگان
چکیده
The algebraic study of formal languages shows thatω-rational languages are exactly the sets recognizable by finite ω-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 ω-rational language to the ω-semigroup context. More precisely, we first define a reduction relation on finite pointed ω-semigroups by means of a Wadge-like infinite two-player game. The collection of these algebraic structures ordered by this reduction is then proven to be isomorphic to the Wagner hierarchy, namely a decidable and well-founded partial ordering of width 2 and height ω.
منابع مشابه
A game theoretical approach to the algebraic counterpart of the Wagner hierarchy: Part I
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