TY - JOUR

T1 - The complexity of linear-time temporal logic over the class of ordinals

AU - St́ephane, Demri

AU - Rabinovich, Alexander

PY - 2010

Y1 - 2010

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 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 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 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 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.

KW - Automaton

KW - Linear-time temporal logic

KW - Ordinal

KW - Polynomial space

UR - http://www.scopus.com/inward/record.url?scp=79951890031&partnerID=8YFLogxK

U2 - 10.2168/LMCS-6(4:9)2010

DO - 10.2168/LMCS-6(4:9)2010

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AN - SCOPUS:79951890031

SN - 1860-5974

VL - 6

SP - 1

EP - 25

JO - Logical Methods in Computer Science

JF - Logical Methods in Computer Science

IS - 4

ER -