The algebraic study of formal languages shows that ω-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 ω . © 2008 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Cabessa, J., & Duparc, J. (2008). The algebraic counterpart of the Wagner hierarchy. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5028 LNCS, pp. 100–109). https://doi.org/10.1007/978-3-540-69407-6_11
Mendeley helps you to discover research relevant for your work.