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Article Dans Une Revue International Journal of Foundations of Computer Science Année : 2007

Reasoning about transfinite sequences

Résumé

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 and model-checking for the logics working on ω k-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.
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Dates et versions

hal-03189812 , version 1 (05-04-2021)

Identifiants

Citer

Stéphane Demri, David Nowak. Reasoning about transfinite sequences. International Journal of Foundations of Computer Science, 2007, 18 (1), pp.87--112. ⟨10.1142/S0129054107004589⟩. ⟨hal-03189812⟩
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