TY - GEN

T1 - The complexity of temporal logic with until and since over ordinals

AU - Demri, Stéphane

AU - Rabinovich, Alexander

PY - 2007

Y1 - 2007

N2 - 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 thanks to 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 α and a formula, we can decide in PSPACE whether the formula has a model over α. In order to show these results, we introduce a class of simple ordinal automata, as expressive as Büchi 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.

AB - 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 thanks to 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 α and a formula, we can decide in PSPACE whether the formula has a model over α. In order to show these results, we introduce a class of simple ordinal automata, as expressive as Büchi 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.

UR - http://www.scopus.com/inward/record.url?scp=38149052173&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-75560-9_38

DO - 10.1007/978-3-540-75560-9_38

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AN - SCOPUS:38149052173

SN - 9783540755586

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 531

EP - 545

BT - Logic for Programming, Artificial Intelligence, and Reasoning - 14th International Conference, LPAR 2007, Proceedings

PB - Springer Verlag

T2 - 14th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR 2007

Y2 - 15 October 2007 through 19 October 2007

ER -