Branching-time logics repeatedly referring to states

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.
Keywords Branching time logic  Hybrid logic  Temporal logic  Complexity  CTL  Pebble automata  Alternating tree automata  Symmetric automata
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DOI 10.1007/s10849-009-9093-x
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Weakly Definable Relations and Special Automata.Michael O. Rabin - 1975 - Journal of Symbolic Logic 40 (4):622-623.

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