Abstract
We consider three properties that can be verified by the rational subsets of a monoid M: to coincide with the recognizable subsets of M, to coincide with the unambiguous rational subsets of M, to form a boolean algebra. We study what connections exist between these properties. We build a monoid in which rational subsets are recognizable (and thus form a boolean algebra), but are not all unambiguous and a monoid in which rational subsets are unambiguous but do not form a boolean algebra. We show that the class of monoids the rational subsets of which are recognizable and unambiguous is not closed by finitely generated submonoids.
This work has been partially supported by the PRC Mathématiques et Informatique.
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© 1990 Springer-Verlag Berlin Heidelberg
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Pelletier, M. (1990). Boolean closure and unambiguity of rational sets. In: Paterson, M.S. (eds) Automata, Languages and Programming. ICALP 1990. Lecture Notes in Computer Science, vol 443. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0032055
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DOI: https://doi.org/10.1007/BFb0032055
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Print ISBN: 978-3-540-52826-5
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