License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.TIME.2020.17
URN: urn:nbn:de:0030-drops-129850
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12985/
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Bednarczyk, Bartosz ; Witkowski, Piotr

A Note on C² Interpreted over Finite Data-Words

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LIPIcs-TIME-2020-17.pdf (0.5 MB)

Abstract

We consider the satisfiability problem for the two-variable fragment of first-order logic extended with counting quantifiers, interpreted over finite words with data, denoted here with C²[≤ , succ, ∼, π_bin]. In our scenario, we allow for using arbitrary many uninterpreted binary predicates from π_bin, two navigational predicates ≤ and succ over word positions as well as a data-equality predicate ∼. We prove that the obtained logic is undecidable, which contrasts with the decidability of the logic without counting by Montanari, Pazzaglia and Sala [Angelo Montanari et al., 2016]. We supplement our results with decidability for several sub-fragments of C²[≤ , succ, ∼, π_bin], e.g. without binary predicates, without successor succ, or under the assumption that the total number of positions carrying the same data value in a data-word is bounded by an a priori given constant.

BibTeX - Entry

@InProceedings{bednarczyk_et_al:LIPIcs:2020:12985,
  author =	{Bartosz Bednarczyk and Piotr Witkowski},
  title =	{{A Note on C² Interpreted over Finite Data-Words}},
  booktitle =	{27th International Symposium on Temporal Representation and Reasoning (TIME 2020)},
  pages =	{17:1--17:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-167-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{178},
  editor =	{Emilio Mu{\~n}oz-Velasco and Ana Ozaki and Martin Theobald},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12985},
  URN =		{urn:nbn:de:0030-drops-129850},
  doi =		{10.4230/LIPIcs.TIME.2020.17},
  annote =	{Keywords: Two-variable logic, data-words, VASS, decidability, undecidability, counting}
}

Keywords: Two-variable logic, data-words, VASS, decidability, undecidability, counting
Collection: 27th International Symposium on Temporal Representation and Reasoning (TIME 2020)
Issue Date: 2020
Date of publication: 15.09.2020

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