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oai:drops-oai.dagstuhl.de:5443 2024-03-06T10:36:28Z ddc:004 open_access

Two-variable Logic with Counting and a Linear Order Charatonik, Witold Witkowski, Piotr Two-variable logic counting quantifiers linear order satisfiability complexity We study the finite satisfiability problem for the two-variable fragment of the first-order logic extended with counting quantifiers (C2) and interpreted over linearly ordered structures. We show that the problem is undecidable in the case of two linear orders (in presence of two other binary symbols). In the case of one linear order it is NEXPTIME-complete, even in presence of the successor relation. Surprisingly, the complexity of the problem explodes when we add one binary symbol more: C2 with one linear order and its successor, in presence of other binary predicate symbols, is decidable, but it is as expressive (and as complex) as Vector Addition Systems. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Witold Charatonik and Piotr Witkowski 2015 Is Part Of LIPIcs, Volume 41, 24th EACSL Annual Conference on Computer Science Logic (CSL 2015) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2015.631 urn:nbn:de:0030-drops-54436 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2015.631 eng https://creativecommons.org/licenses/by/3.0/legalcode