Journal of Logic, Language and Information

, Volume 18, Issue 4, pp 593–624

Branching-Time Logics Repeatedly Referring to States


DOI: 10.1007/s10849-009-9093-x

Cite this article as:
Weber, V. J of Log Lang and Inf (2009) 18: 593. doi:10.1007/s10849-009-9093-x


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.


Branching time logicHybrid logicTemporal logicComplexityCTLPebble automataAlternating tree automataSymmetric automata

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Fakultät für InformatikTechnische Universität DortmundDortmundGermany