Charatonik, Witold and Witkowski, Piotr - Two-variable Logic with Counting and a Linear Order

lmcs:1640 - Logical Methods in Computer Science, June 23, 2016, Volume 12, Issue 2
Two-variable Logic with Counting and a Linear Order

Authors: Charatonik, Witold and Witkowski, Piotr

We study the finite satisfiability problem for the two-variable fragment of 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 the presence of two other binary symbols). In the case of one linear order it is NEXPTIME-complete, even in the 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 in the presence of other binary predicate symbols is equivalent, under elementary reductions, to the emptiness problem for multicounter automata.


Source : oai:arXiv.org:1604.06038
DOI : 10.2168/LMCS-12(2:8)2016
Volume: Volume 12, Issue 2
Published on: June 23, 2016
Submitted on: November 2, 2015
Keywords: Computer Science - Logic in Computer Science


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