Improved upper and lower bounds for modal logics of programs
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Structural complexity 2
Journal of the ACM (JACM)
Reasoning about The Past with Two-Way Automata
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
EXPSPACE-Complete Variant of Guarded Fragment with Transitivity
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Tableaux and Algorithms for Propositional Dynamic Logic with Converse
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
The Two-Variable Guarded Fragment with Transitive Relations
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
On the Decision Problem for the Guarded Fragment with Transitivity
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
The two-variable guarded fragment with transitive guards is 2EXPTIME-hard
FOSSACS'03/ETAPS'03 Proceedings of the 6th International conference on Foundations of Software Science and Computation Structures and joint European conference on Theory and practice of software
Results on the guarded fragment with equivalence or transitive relations
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
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We investigate the complexity of the satisfiability problem for the two-variable guarded fragment with transitive guards. We prove that the satisfiability problem for the monadic version of this logic without equality is 2EXPTIME-hard. It is in fact 2EXPTIME-complete, since as shown by Szwast and Tendera, the whole guarded fragment with transitive guards is in 2EXPTIME. We also introduce a new logic--the guarded fragment with one-way transitive guards and prove that the satisfiability problem for the two-variable version of this logic is EXPSPACE-complete. The two-variable guarded fragment with transitive guards can be seen as a counterpart of some branching temporal logics with both future and past operators, while the two-variable guarded fragment with one-way transitive guards corresponds to some branching temporal logics without past operators. Therefore, our results reveal the difference in the complexity of the reasoning about the future only and both the future and the past, in the two-variable guarded fragment with transitive guards.