Syntactic Semiring of a Language

Authors:
Libor Polák
Affiliations:
-
Venue:
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Year:
2001

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Abstract

A classical construction assigns to any language its (ordered) syntactic monoid. Recently the author defined the so-called syntactic semiring of a language. We discuss here the relationships between those two structures. Pin's refinement of Eilenberg theorem gives a one-to-one correspondence between positive varieties of rational languages and pseudovarieties of ordered monoids. The author's modification uses so-called conjunctive varieties of rational languages and pseudovarieties of idempotent semirings. We present here also several examples of our varieties of languages.