Syntactic Semiring of a Language

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Authors

POLÁK Libor

Year of publication 2001
Type Article in Proceedings
Conference Mathematical foundations of computer science 2001
MU Faculty or unit

Faculty of Informatics

Citation
Field General mathematics
Keywords syntactic semiring; rational languages
Description 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.
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