Demri, Stephane and Rabinovich, Alexander - The complexity of linear-time temporal logic over the class of ordinals

lmcs:1230 - Logical Methods in Computer Science, December 21, 2010, Volume 6, Issue 4
The complexity of linear-time temporal logic over the class of ordinals

Authors: Demri, Stephane and Rabinovich, Alexander

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.


Source : oai:arXiv.org:1009.5206
DOI : 10.2168/LMCS-6(4:9)2010
Volume: Volume 6, Issue 4
Published on: December 21, 2010
Submitted on: February 23, 2010
Keywords: Computer Science - Logic in Computer Science,F.4.1, F.3.1., F.2.2


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