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arXiv · 1810.09142

Complexity and Expressivity of Branching- and Alternating-Time Temporal Logics with Finitely Many Variables

Mikhail Rybakov·Dmitry Shkatov
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Abstract

We show that Branching-time temporal logics CTL and CTL*, as well as Alternating-time temporal logics ATL and ATL*, are as semantically expressive in the language with a single propositional variable as they are in the full language, i.e., with an unlimited supply of propositional variables. It follows that satisfiability for CTL, as well as for ATL, with a single variable is EXPTIME-complete, while satisfiability for CTL*, as well as for ATL*, with a single variable is 2EXPTIME-complete,--i.e., for these logics, the satisfiability for formulas with only one variable is as hard as satisfiability for arbitrary formulas.

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Mikhail Rybakov, Dmitry Shkatov. 2018-10-22. Complexity and Expressivity of Branching- and Alternating-Time Temporal Logics with Finitely Many Variables. https://doi.org/10.1007/978-3-030-02508-3_21

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