A game theoretical approach to the algebraic counterpart of the Wagner hierarchy : part II
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 43 (2009) no. 3, pp. 463-515.

The algebraic counterpart of the Wagner hierarchy consists of a well-founded and decidable classification of finite pointed ω-semigroups of width 2 and height ω ω . 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 ω-semigroups allowing to compute their precise Wagner degrees. The Wagner degree of any ω-rational language can therefore be computed directly on its syntactic image. We then show how to build a finite pointed ω-semigroup of any given Wagner degree. We finally describe the algebraic invariants characterizing every degree of this hierarchy.

DOI: 10.1051/ita/2009007
Classification: O3D55,  20M35,  68Q70,  91A65
Keywords: ω-automata, ω-rational languages, ω-semigroups, infinite games, hierarchical games, Wadge game, Wadge hierarchy, Wagner hierarchy
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Cabessa, Jérémie; Duparc, Jacques. A game theoretical approach to the algebraic counterpart of the Wagner hierarchy : part II. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 43 (2009) no. 3, pp. 463-515. doi : 10.1051/ita/2009007. http://www.numdam.org/articles/10.1051/ita/2009007/

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