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
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Deciding Regular Grammar Logics with Converse Through First-Order Logic
Journal of Logic, Language and Information
On the complexity of the two-variable guarded fragment with transitive guards
Information and Computation
Decidability of the Guarded Fragment with the Transitive Closure
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
On finite satisfiability of the guarded fragment with equivalence or transitive guards
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
On the finite satisfiability problem for the guarded fragment with transitivity
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Counting in the two variable guarded logic with transitivity
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Results on the guarded fragment with equivalence or transitive relations
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
Querying the guarded fragment with transitivity
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
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We prove that the satisfiability problem for the two-variable guarded fragment with transitive guards GF2 +TG is 2EXPTIME-hard. This result closes the open questions left in [4], [17]. In fact, we show 2EXPTIME-hardness of minGF2 + TG, a fragment of GF2 + TG without equality and with just one transitive relation ???, which is the only non-unary symbol allowed. Our lower bound for minGF2 + TG matches the upper bound for the whole guarded fragment with transitive guards and the unrestricted number of variables GF + TG given by Szwast and Tendera [17], so in fact GF2 +TG is 2EXPTIME-complete. It is surprising that the complexity of minGF2 + TG is higher then the complexity of the variant with one-way transitive guards GF2 + ???TG [9]. The latter logic appears naturally as a counterpart of temporal logics without past operators.