A Semiring-Semimodule Generalization of ω-Context-Free Languages

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We develop an algebraic theory on semiring-semimodule pairs for ω-context-free languages. We define ω-algebraic systems and characterize their solutions of order k by behaviors of algebraic finite automata. These solutions are then set in correspondence to ω-context-free languages.

Partially supported by Aktion Österreich-Ungarn, Wissenschafts- und Erziehungskooperation, Projekt 53ÖU1. Additionally, the first author was supported, in part, by the National Foundation of Hungary for Scientific Research, grant T 35163.