The Complexity of Satisfiability for Fragments of CTL and CTL*;

Authors:
Arne Meier;Martin Mundhenk;Michael Thomas;Heribert Vollmer
Affiliations:
Theoretische Informatik, Gottfried Wilhelm Leibniz Universität, Appelstr. 4, 30167 Hannover, Germany;Institut für Informatik, Friedrich-Schiller-Universität, 07737 Jena, Germany;Theoretische Informatik, Gottfried Wilhelm Leibniz Universität, Appelstr. 4, 30167 Hannover, Germany;Theoretische Informatik, Gottfried Wilhelm Leibniz Universität, Appelstr. 4, 30167 Hannover, Germany
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2008

Citing 12
Cited 5

The complexity of propositional linear temporal logics

Journal of the ACM (JACM)
Automatic verification of finite-state concurrent systems using temporal logic specifications

ACM Transactions on Programming Languages and Systems (TOPLAS)
Improved upper and lower bounds for modal logics of programs

STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Temporal and modal logic

Handbook of theoretical computer science (vol. B)
About the expressive power of CTL combinators

Information Processing Letters
Theories of computability

Theories of computability
Gap-languages and log-time complexity classes

Theoretical Computer Science
Introduction to Circuit Complexity: A Uniform Approach

Introduction to Circuit Complexity: A Uniform Approach
"Sometimes" and "not never" revisited: on branching versus linear time (preliminary report)

POPL '83 Proceedings of the 10th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
The complexity of theorem-proving procedures

STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Past is for free: on the complexity of verifying linear temporal properties with past

Acta Informatica
The complexity of generalized satisfiability for linear temporal logic

FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures

The complexity of propositional implication

Information Processing Letters
A decidable spatial logic with cone-shaped cardinal directions

CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Complexity results for modal dependence logic

CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
The Complexity of Reasoning for Fragments of Autoepistemic Logic

ACM Transactions on Computational Logic (TOCL)
Complexity Results for Modal Dependence Logic

Studia Logica

Quantified Score

Hi-index	0.00

Visualization

Abstract

The satisfiability problems for CTL and CTL^@? are known to be EXPTIME-complete, resp. 2EXPTIME-complete (Fischer and Ladner (1979), Vardi and Stockmeyer (1985)). For fragments that use less temporal or propositional operators, the complexity may decrease. This paper undertakes a systematic study of satisfiability for CTL- and CTL^@?-formulae over restricted sets of propositional and temporal operators. We show that restricting the temporal operators yields satisfiability problems complete for 2EXPTIME, EXPTIME, PSPACE, and NP. Restricting the propositional operators either does not change the complexity (as determined by the temporal operators), or yields very low complexity like NC^1, TC^0, or NLOGTIME.