Deterministic Automata and Extensions of Weak MSO

Authors Mikolaj Bojanczyk, Szymon Torunczyk

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Mikolaj Bojanczyk
Szymon Torunczyk

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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)


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.
  • Deterministic automata
  • Weak MSO
  • min-automata
  • max-automata
  • BS-automata


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