Reasoning About Periodicity on Infinite Words

Characterization of temporal properties is the original purpose of inventing of temporal logics. In this paper, we show that the property like “some event holds periodically” is not omega-regular. Such property is called “periodicity”, which plays an important role in task scheduling and system design. To give a characterization of periodicity, we present the logic QPLTL, which is an extension of LTL via adding quantified step variables. Based on the decomposition theorem, we show that the satisfiability problem of QPLTL is PSPACE-complete.

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