An Algebraic Generalization of ω-Regular Languages
- Cite this paper as:
- Ésik Z., Kuich W. (2004) An Algebraic Generalization of ω-Regular Languages. In: Fiala J., Koubek V., Kratochvíl J. (eds) Mathematical Foundations of Computer Science 2004. MFCS 2004. Lecture Notes in Computer Science, vol 3153. Springer, Berlin, Heidelberg
This paper continues the algebraic theory of Ésik, Kuich  on semiring-semimodule pairs and quemirings that is applicable to languages that contain finite and infinite words. The main advantage is that we get rid of the idempotency assumption for the semimodule needed at several places in Ésik, Kuich .
Additionally, we consider linear systems as a generalization of rightlinear grammars. Moreover, we develop an algorithm that constructs, for a given finite automaton, an equivalent one without ε-moves.
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