The complexity of propositional linear temporal logics
Journal of the ACM (JACM)
POPL '88 Proceedings of the 15th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The complexity of propositional linear temporal logics in simple cases
Information and Computation
The temporal logic of programs
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
On the complexity of omega -automata
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Bounded-variable fragments of hybrid logics
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
On the complexity of hybrid logics with binders
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
Hybrid and first-order complete extensions of CaRet
TABLEAUX'11 Proceedings of the 20th international conference on Automated reasoning with analytic tableaux and related methods
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Full linear-time hybrid logic (HL) is a non-elementary and equally expressive extension of standard LTL+ past obtained by adding the well-known binder operators 茂戮驴 and 茂戮驴. We investigate complexity and succinctness issues for HLin terms of the number of variables and nesting depth of binder modalities. First, we present directautomata-theoretic decision procedures for satisfiability and model-checking of HL, which require space of exponential height equal to the nesting depth of binder modalities. The proposed algorithms are proved to be asymptotically optimal by providing matching lower bounds. Second, we show that for the one-variable fragment of HL, the considered problems are elementary and, precisely, Expspace-complete. Finally, we show that for all 0 ≤ hk, there is a succinctness gap between the fragments HLkand HLhwith binder nesting depth at most kand h, respectively, of exponential height equal to k茂戮驴 h.