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.
@InProceedings{bojanczyk_et_al:LIPIcs.FSTTCS.2009.2308, author = {Bojanczyk, Mikolaj and Torunczyk, Szymon}, title = {{Deterministic Automata and Extensions of Weak MSO}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science}, pages = {73--84}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-13-2}, ISSN = {1868-8969}, year = {2009}, volume = {4}, editor = {Kannan, Ravi and Narayan Kumar, K.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2308}, URN = {urn:nbn:de:0030-drops-23081}, doi = {10.4230/LIPIcs.FSTTCS.2009.2308}, annote = {Keywords: Deterministic automata, Weak MSO, min-automata, max-automata, BS-automata} }
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