We consider the temporal logic with since and until modalities. This tempo- ral 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 count- able ordinaland a formula, we can decide in pspace whether the formula has a model over �. In order to show these results, we introduce a class of simple ordinal automata, as expressive as Buchi ordinal automata. The pspace upper bound for the satisfiability prob- lem of the temporal logic is obtained through a reduction to the nonemptiness problem for the simple ordinal automata.
['Stéphane Demri', 'Alexander Rabinovich']
THE COMPLEXITY OF LINEAR-TIME TEMPORAL LOGIC OVER THE CLASS OF ORDINALS