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Branching–Time Logics Repeatedly Referring to States

Volker Weber
Journal of Logic, Language, and Information
Vol. 18, No. 4, Hybrid Logic: Dedicated to the Memory of Volker Weber (Autumn, 2009), pp. 593-624
Published by: Springer
Stable URL: http://www.jstor.org/stable/40345511
Page Count: 32
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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 2EXPTIM E-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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