The complexity of propositional linear temporal logics
Journal of the ACM (JACM)
Propositional dynamic logic of flowcharts
Information and Control
Finite automata, formal logic, and circuit complexity
Finite automata, formal logic, and circuit complexity
Reasoning about infinite computations
Information and Computation
Regular languages defined with generalized quantifiers
Information and Computation
First-order logic with two variables and unary temporal logic
Information and Computation - Special issue: LICS'97
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Vectorial languages and linear temporal logic
Theoretical Computer Science
Reasoning about infinite computation paths
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
From Philosophical to Industrial Logics
ICLA '09 Proceedings of the 3rd Indian Conference on Logic and Its Applications
TIME '10 Proceedings of the 2010 17th International Symposium on Temporal Representation and Reasoning
Expressive Completeness for LTL With Modulo Counting and Group Quantifiers
Electronic Notes in Theoretical Computer Science (ENTCS)
| Hi-index | 0.00 |
It is well known that modelchecking and satisfiability of Linear Temporal Logic (LTL) are Pspace-complete. Wolper showed that with grammar operators, this result can be extended to increase the expressiveness of the logic to all regular languages. Other ways of extending the expressiveness of LTL using modular and group modalities have been explored by Baziramwabo, McKenzie and Thérien, which are expressively complete for regular languages recognized by solvable monoids and for all regular languages, respectively. In all the papers mentioned, the numeric constants used in the modalities are in unary notation. We show that in some cases (such as the modular and symmetric group modalities and for threshold counting) we can use numeric constants in binary notation, and still maintain the Pspace upper bound. Adding modulo counting to LTL[F] (with just the unary future modality) already makes the logic Pspace-hard. We also consider a restricted logic which allows only the modulo counting of length from the beginning of the word. Its satisfiability is Σ3P -complete.