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Two-Variable Logic with Counting and Trees

Two-Variable Logic with Counting and Trees Two-Variable Logic with Counting and Trees WITOLD CHARATONIK and PIOTR WITKOWSKI, University of Wroclaw We consider the two-variable logic with counting quantifiers (C2 ) interpreted over finite structures that contain two forests of ranked trees. This logic is strictly more expressive than standard C2 and it is no longer a fragment of first-order logic. In particular, it can express that a structure is a ranked tree, a cycle, or a connected graph of bounded degree. It is also strictly more expressive than first-order logic with two variables and two successor relations of two finite linear orders. We present a decision procedure for the satisfiability problem for this logic. The procedure runs in NEXPTIME, which is optimal since the satisfiability problem for plain C2 is NEXPTIME-complete. CCS Concepts: completeness r Theory of computation Finite Model Theory; Problems, reductions and Additional Key Words and Phrases: Counting quantifier, satisfiability, tree, two-variable logic ACM Reference Format: Witold Charatonik and Piotr Witkowski. 2016. Two-variable logic with counting and trees. ACM Trans. Comput. Logic 17, 4, Article 31 (October 2016), 27 pages. DOI: http://dx.doi.org/10.1145/2983622 1. INTRODUCTION 1.1. Two-Variable Logics First-order logic with two variables (for short, two-variable logic, FO2 ) is, in addition to http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

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Publisher
Association for Computing Machinery
Copyright
Copyright © 2016 by ACM Inc.
ISSN
1529-3785
DOI
10.1145/2983622
Publisher site
See Article on Publisher Site

Abstract

Two-Variable Logic with Counting and Trees WITOLD CHARATONIK and PIOTR WITKOWSKI, University of Wroclaw We consider the two-variable logic with counting quantifiers (C2 ) interpreted over finite structures that contain two forests of ranked trees. This logic is strictly more expressive than standard C2 and it is no longer a fragment of first-order logic. In particular, it can express that a structure is a ranked tree, a cycle, or a connected graph of bounded degree. It is also strictly more expressive than first-order logic with two variables and two successor relations of two finite linear orders. We present a decision procedure for the satisfiability problem for this logic. The procedure runs in NEXPTIME, which is optimal since the satisfiability problem for plain C2 is NEXPTIME-complete. CCS Concepts: completeness r Theory of computation Finite Model Theory; Problems, reductions and Additional Key Words and Phrases: Counting quantifier, satisfiability, tree, two-variable logic ACM Reference Format: Witold Charatonik and Piotr Witkowski. 2016. Two-variable logic with counting and trees. ACM Trans. Comput. Logic 17, 4, Article 31 (October 2016), 27 pages. DOI: http://dx.doi.org/10.1145/2983622 1. INTRODUCTION 1.1. Two-Variable Logics First-order logic with two variables (for short, two-variable logic, FO2 ) is, in addition to

Journal

ACM Transactions on Computational Logic (TOCL)Association for Computing Machinery

Published: Nov 15, 2016

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