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arXiv · 1009.5206

The complexity of linear-time temporal logic over the class of ordinals

Stephane Demri·Alexander Rabinovich
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Abstract

We consider the temporal logic with since and until modalities. This temporal logic is expressively equivalent over the class of ordinals to first-order logic by Kamp's theorem. We show that it has a PSPACE-complete satisfiability problem over the class of ordinals. Among the consequences of our proof, we show that given the code of some countable ordinal alpha and a formula, we can decide in PSPACE whether the formula has a model over alpha. In order to show these results, we introduce a class of simple ordinal automata, as expressive as B\"uchi ordinal automata. The PSPACE upper bound for the satisfiability problem of the temporal logic is obtained through a reduction to the nonemptiness problem for the simple ordinal automata.

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Stephane Demri, Alexander Rabinovich. 2010-09-27. The complexity of linear-time temporal logic over the class of ordinals. https://doi.org/10.2168/lmcs-6(4%3A9)2010

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