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Branching-Time Logics Repeatedly Referring to States

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Abstract

While classical temporal logics lose track of a state as soon as a temporal operator is applied, several branching-time logics able to repeatedly refer to a state have been introduced in the literature. We study such logics by introducing a new formalism, hybrid branching-time logics, subsuming the other approaches and making the ability to refer to a state more explicit by assigning a name to it. We analyze the expressive power of hybrid branching-time logics and the complexity of their satisfiability problem. As main result, the satisfiability problem for the hybrid versions of several branching-time logics is proved to be 2EXPTIME-complete. To prove the upper bound, the automata-theoretic approach to branching-time logics is extended to hybrid logics. As a result of independent interest, the nonemptiness problem for alternating one-pebble Büchi tree automata is shown to be 2EXPTIME-complete. A common property of the logics studied is that they refer to only one state. This restriction is crucial: The ability to refer to more than one state causes a nonelementary blow-up in complexity. In particular, we prove that satisfiability for NCTL* has nonelementary complexity.

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  1. Fakultät für Informatik, Technische Universität Dortmund, 44221, Dortmund, Germany

    Volker Weber

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  1. Volker Weber
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Weber, V. Branching-Time Logics Repeatedly Referring to States. J of Log Lang and Inf 18, 593–624 (2009). https://doi.org/10.1007/s10849-009-9093-x

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