David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Journal of Logic, Language and Information 18 (4):593-624 (2009)
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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References found in this work BETA
Carlos Areces, Patrick Blackburn & Maarten Marx (2001). Hybrid Logics: Characterization, Interpolation and Complexity. Journal of Symbolic Logic 66 (3):977-1010.
Michael O. Rabin (1975). Weakly Definable Relations and Special Automata. Journal of Symbolic Logic 40 (4):622-623.
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