Filter by type:

Sort by year

Modulo Counting on Words and Trees

Bartosz Bednarczyk, Witold Charatonik
Conference Papers Proceedings of the 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2017, December 11–15, 2017, Kanpur, India. LIPIcs 93, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik 2017, pages 12:1–12:16.

Abstract

We consider the satisfiability problem for the two-variable fragment of the first-order logic extended with modulo counting quantifiers and interpreted over finite words or trees. We prove a small-model property of this logic, which gives a technique for deciding the satisfiability problem. In the case of words this gives a new proof of EXPSPACE upper bound, and in the case of trees it gives a 2EXPTIME algorithm. This algorithm is optimal: we prove a matching lower bound by a generic reduction from alternating Turing machines working in exponential space; the reduction involves a development of a new version of tiling games.

Extending Two-Variable Logic on Trees

Bartosz Bednarczyk, Witold Charatonik, Emanuel Kieroński
Conference Papers Proceedings of the 26th EACSL Annual Conference on Computer Science Logic, CSL 2017, August 20-24, 2017, Stockholm, Sweden. LIPIcs 82, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik 2017, pages 11:1-11:20

Abstract

The finite satisfiability problem for the two-variable fragment of first-order logic interpreted over trees was recently shown to be ExpSpace-complete. We consider two extensions of this logic. We show that adding either additional binary symbols or counting quantifiers to the logic does not affect the complexity of the finite satisfiability problem. However, combining the two extensions and adding both binary symbols and counting quantifiers leads to an explosion of this complexity. We also compare the expressive power of the two-variable fragment over trees with its extension with counting quantifiers. It turns out that the two logics are equally expressive, although counting quantifiers do add expressive power in the restricted case of unordered trees.

On One Variable Fragment of First Order Logic with Modulo Counting Quantifier

Bartosz Bednarczyk
Conference Papers Proceedings of ESSLLI 2017 Student Session, 29th European Summer School in Logic, Language & Information, July 17-28, 2017, Toulouse, France, pages 7-13

Abstract

We consider the one-variable fragment of first-order logic extended with modulo counting quantifiers. We prove NPTime-completeness of such fragment by presenting an optimal algorithm for solving its finite satisfiability problem.

Satisfiability of the Two-Variable Fragment of First-Order Logic with counting quantifiers over finite trees

Bartosz Bednarczyk
Bachelor Thesis Dissertation advisor: prof. dr hab. Witold Charatonik, Date of defence: Feb. 15, 2017

Abstract

The finite satisfiability problem for the two-variable fragment of first-order logic interpreted over trees was recently shown to be ExpSpace-complete. We show that adding counting quantifiers to the logic does not affect the complexity of the finite satisfiability problem.