LIPIcs.FSTTCS.2009.2308.pdf
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Deterministic Automata and Extensions of Weak MSO
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IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2009)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS) - License:
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
- Publication Date: 2009-12-14
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Mikolaj Bojanczyk and Szymon Torunczyk. Deterministic Automata and Extensions of Weak MSO. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 73-84, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
https://doi.org/10.4230/LIPIcs.FSTTCS.2009.2308
Abstract
We introduce a new class of automata on infinite words, called
min-automata. We prove that min-automata have the same expressive
power as weak monadic second-order logic (weak MSO) extended with a new
quantifier, the recurrence quantifier. These results are dual to a
framework presented in \cite{max-automata}, where max-automata were proved equivalent
to weak MSO extended with an unbounding
quantifier. We also present a general framework, which tries to
explain which types of automata on infinite words correspond to
extensions of weak MSO. As another example for the usefulness framework,
apart from min- and max-automata, we define an extension of weak MSO
with a quantifier that talks about ultimately periodic sets.
Subject Classification
Keywords
- Deterministic automata
- Weak MSO
- min-automata
- max-automata
- BS-automata
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