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

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

2010-09-27

arxiv.org/abs/1009.5206v2

LMCS 6 (4:9) 2010

Computer Science

Logic in Computer Science

Accepted for publication in LMCS

Scientific paper

10.2168/LMCS-6(4:9)2010

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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