Complexity of two-variable logic on finite trees

Authors:
Saguy Benaim;Michael Benedikt;Witold Charatonik;Emanuel Kieroński;Rastislav Lenhardt;Filip Mazowiecki;James Worrell
Affiliations:
University of Oxford, UK;University of Oxford, UK;University of Wrocław, Poland;University of Wrocław, Poland;University of Oxford, UK;University of Warsaw, Poland;University of Oxford, UK
Venue:
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
Year:
2013

Citing 9
Cited 1

Languages, automata, and logic

Handbook of formal languages, vol. 3
EXPSPACE-Complete Variant of Guarded Fragment with Transitivity

STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
First-order logic with two variables and unary temporal logic

Information and Computation - Special issue: LICS'97
XPath satisfiability in the presence of DTDs

Journal of the ACM (JACM)
XPath leashed

ACM Computing Surveys (CSUR)
Two-variable logic on data trees and XML reasoning

Journal of the ACM (JACM)
Results on the guarded fragment with equivalence or transitive relations

CSL'05 Proceedings of the 19th international conference on Computer Science Logic
Expressiveness and succinctness of first-order logic on finite words

Expressiveness and succinctness of first-order logic on finite words
Verification of Two-Variable Logic Revisited

QEST '12 Proceedings of the 2012 Ninth International Conference on Quantitative Evaluation of Systems

Two-Variable Logic with Counting and Trees

LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

Verification of properties expressed in the two-variable fragment of first-order logic FO2 has been investigated in a number of contexts. The satisfiability problem for FO2 over arbitrary structures is known to be NEXPTIME-complete, with satisfiable formulas having exponential-sized models. Over words, where FO2 is known to have the same expressiveness as unary temporal logic, satisfiability is again NEXPTIME-complete. Over finite labelled ordered trees FO2 has the same expressiveness as navigational XPath, a popular query language for XML documents. Prior work on XPath and FO2 gives a 2EXPTIME bound for satisfiability of FO2 over trees. This work contains a comprehensive analysis of the complexity of FO2 on trees, and on the size and depth of models. We show that the exact complexity varies according to the vocabulary used, the presence or absence of a schema, and the encoding of labels on trees. We also look at a natural restriction of FO2, its guarded version, GF2. Our results depend on an analysis of types in models of FO2 formulas, including techniques for controlling the number of distinct subtrees, the depth, and the size of a witness to satisfiability for FO2 sentences over finite trees.