A GAME THEORETICAL APPROACHTO THE ALGEBRAIC COUNTERPARTOF THE WAGNER HIERARCHY: PART II

The algebraic counterpart of the Wagner hierarchy consistsof a well-founded and decidable classification of finite pointedω-semigroups of width 2 and height ωω. This paper completes thedescription of this algebraic hierarchy. We first give a purely algebraicdecidability procedure of this partial ordering by introducing a graphrepresentation of finite pointed ω-semigroups allowing to compute theirprecise Wagner degrees. The Wagner degree of any ω-rational languagecan therefore be computed directly on its syntactic image. We thenshow how to build a finite pointed ω-semigroup of any given Wagnerdegree. We finally describe the algebraic invariants characterizing everydegree of this hierarchy