Closure Properties of Locally Finite Omega Languages
Olivier Finkel (ELM)
TL;DR
This paper investigates the closure properties of locally finite omega languages, showing they are not closed under intersection or complementation, thus answering a question posed by Ressayre.
Contribution
It provides the first proof that the class LOC_omega is not closed under intersection and complementation.
Findings
LOC_omega is not closed under intersection
LOC_omega is not closed under complementation
Answers a question posed by Ressayre about closure properties
Abstract
Locally finite omega languages were introduced by Ressayre in [Journal of Symbolic Logic, Volume 53, No. 4, p.1009-1026]. They generalize omega languages accepted by finite automata or defined by monadic second order sentences. We study here closure properties of the family LOC_omega of locally finite omega languages. In particular we show that the class LOC_omega is neither closed under intersection nor under complementation, giving an answer to a question of Ressayre.
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Taxonomy
Topicssemigroups and automata theory · Logic, programming, and type systems · Advanced Algebra and Logic