The complexity of propositional linear temporal logics
Journal of the ACM (JACM)
On the synthesis of a reactive module
POPL '89 Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Specifying real-time properties with metric temporal logic
Real-Time Systems
Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Real-time logics: complexity and expressiveness
Information and Computation - Special issue: selections from 1990 IEEE symposium on logic in computer science
Parametric temporal logic for “model measuring”
ACM Transactions on Computational Logic (TOCL)
On the Synthesis of an Asynchronous Reactive Module
ICALP '89 Proceedings of the 16th International Colloquium on Automata, Languages and Programming
Small Progress Measures for Solving Parity Games
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Principles of Model Checking (Representation and Mind Series)
Principles of Model Checking (Representation and Mind Series)
Formal Methods in System Design
Finitary winning in ω-regular games
ACM Transactions on Computational Logic (TOCL)
From LTL to symbolically represented deterministic automata
VMCAI'08 Proceedings of the 9th international conference on Verification, model checking, and abstract interpretation
Parametric metric interval temporal logic
LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
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Parameterized linear temporal logics are extensions of Linear Temporal Logic (LTL) by temporal operators equipped with variables that bound their scope. In model-checking, such specifications were introduced as ''PLTL'' by Alur et al. and as ''PROMPT-LTL'' by Kupferman et al. We show how to determine in doubly-exponential time, whether a player wins a game with PLTL winning condition with respect to some, infinitely many, or all variable valuations. Hence, these problems are not harder than solving LTL games. Furthermore, we present an algorithm with triply-exponential running time to determine optimal variable valuations that allow a player to win a game. Finally, we give doubly-exponential upper and lower bounds on the values of such optimal variable valuations.