On the synthesis of a reactive module
POPL '89 Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A partial approach to model checking
Papers presented at the IEEE symposium on Logic in computer science
Reasoning about infinite computations
Information and Computation
The benefits of relaxing punctuality
Journal of the ACM (JACM)
On the temporal analysis of fairness
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Accessibility in Automata on Scattered Linear Orderings
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Symbolic Controller Synthesis for Discrete and Timed Systems
Hybrid Systems II
Elementary Theory of Ordinals with Addition and Left Translation by omega
DLT '01 Revised Papers from the 5th International Conference on Developments in Language Theory
The complexity of the temporal logic with "until" over general linear time
Journal of Computer and System Sciences
Games for synthesis of controllers with partial observation
Theoretical Computer Science - Logic and complexity in computer science
Alternating automata and the temporal logic of ordinals
Alternating automata and the temporal logic of ordinals
Quantitative Temporal Logics: PSPACE and Below
TIME '05 Proceedings of the 12th International Symposium on Temporal Representation and Reasoning
Logics for Real Time: Decidability and Complexity
Fundamenta Informaticae - Continuous Time Paradigms in Logic and Automata
Quantitative temporal logics over the reals: PSpace and below
Information and Computation
On reachability games of ordinal length
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
Controller synthesis and ordinal automata
ATVA'06 Proceedings of the 4th international conference on Automated Technology for Verification and Analysis
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We introduce a family of temporal logics to specify the behavior of systems with Zeno behaviors. We extend linear-time temporal logic LTL to authorize models admitting Zeno sequences of actions and quantitative temporal operators indexed by ordinals replace the standard next-time and until future-time operators. Our aim is to control such systems by designing controllers that safely work on ω-sequences but interact synchronously with the system in order to restrict their behaviors. We show that the satisfiability problem for the logics working on ωk-sequences is expspace-complete when the integers are represented in binary, and pspace-complete with a unary representation. To do so, we substantially extend standard results about LTL by introducing a new class of succinct ordinal automata that can encode the interaction between the different quantitative temporal operators.