Two-variable Logic with Counting and a Linear Order
نویسندگان
چکیده
منابع مشابه
Two-variable Logic with Counting and a Linear Order
We study the finite satisfiability problem for the two-variable fragment of first-order logic extended with counting quantifiers (C) 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...
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Let C 2 p denote the class of rst order sentences with two variables and with additional quantiiers \there exists exactly (at most, at least) i", for i p, and let C 2 be the union of C 2 p taken over all integers p. We prove that the satissability problem for C 2 1 sentences is NEXPTIME-complete. This strengthens the results by E. Grr adel, Ph. Kolaitis and M. Vardi 15] who showed that the sati...
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Etessami, Vardi and Wilke [5] showed that satisfiability of two-variable first order logic FO[<] on word models is Nexptime-complete. We extend this upper bound to the slightly stronger logic FO[<, succ,≡], which allows checking whether a word position is congruent to r modulo q, for some divisor q and remainder r. If we allow the more powerful modulo counting quantifiers of Straubing, Thérien ...
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The finite satisfiability problem for two-variable logic over structures with unary relations and two order relations is investigated. Firstly, decidability is shown for structures with one total preorder relation and one linear order relation. More specifically, we show that this problem is complete for EXPSPACE. As a consequence, the same upper bound applies to the case of two linear orders. ...
متن کاملA Short Note on Two-Variable Logic with a Linear Order Successor and a Preorder Successor
The finite satisfiability problem of two-variable logic extended by a linear order successor and a preorder successor is shown to be undecidable. The decidability of the finite satisfiability problem of two-variable logic extended by orders and preorders as well as their corresponding successor relations has been currently investigated by several papers [2, 5, 3]. This short note extends [3] wh...
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ژورنال
عنوان ژورنال: Logical Methods in Computer Science
سال: 2016
ISSN: 1860-5974
DOI: 10.2168/lmcs-12(2:8)2016