License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.STACS.2016.21
URN: urn:nbn:de:0030-drops-57223
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Bojanczyk, Mikolaj ; Parys, Pawel ; Torunczyk, Szymon

The MSO+U Theory of (N,<) Is Undecidable

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We consider the logic MSO+U, which is monadic second-order logic extended with the unbounding quantifier. The unbounding quantifier is used to say that a property of finite sets holds for sets of arbitrarily large size. We prove that the logic is undecidable on infinite words, i.e. the MSO+U theory of (N,<) is undecidable. This settles an open problem about the logic, and improves a previous undecidability result, which used infinite trees and additional axioms from set theory.

BibTeX - Entry

  author =	{Mikolaj Bojanczyk and Pawel Parys and Szymon Torunczyk},
  title =	{{The MSO+U Theory of (N,<) Is Undecidable}},
  booktitle =	{33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
  pages =	{21:1--21:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-001-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{47},
  editor =	{Nicolas Ollinger and Heribert Vollmer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-57223},
  doi =		{10.4230/LIPIcs.STACS.2016.21},
  annote =	{Keywords: automata, logic, unbounding quantifier, bounds, undecidability}

Keywords: automata, logic, unbounding quantifier, bounds, undecidability
Collection: 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)
Issue Date: 2016
Date of publication: 16.02.2016

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