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Journal of Logic and Computation 2001 11(2):201-228; doi:10.1093/logcom/11.2.201
© 2001 by Oxford University Press
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Original Article

Which Branching-Time Properties are Effectively Linear?

Orna Grumberg1 and Robert P. Kurshan2

1 Computer Science Department, The Technion, Haifa 32000, Israel. E-mail: orna{at}cs.technion.ac.il 2 Bell Laboratories, Murray Hill, NJ 07974, USA. E-mail: k{at}research.bell-labs.com

We characterize three successively more restrictive classes of ‘effectively linear’ CTL* formulas, with and without fairness: the equi-linear formulas, which do not distinguish among models with the same language, the sub-linear formulas, which are preserved under model language inclusion and the strong linear formulas, which are characterized by a given {omega}-regular language. Moreover, strong linearity characterizes those CTL* formulas equivalent to LTL formulas. This taxonomy helps to clarify the expressive distinctions between CTL*, LTL and {omega}-regular languages. It has also practical implications. Verification tools based on language inclusion can handle any CTL* formula which is equi-linear, for purposes of model checking, and sub-linear for purposes of abstraction. Furthermore, minimization techniques that preserve the subset of CTL* which consists of only effectively linear formulas, result in smaller structures than bisimulation minimization.

Keywords: Temporal logic; linear temporal logic; branching temporal logic; fairness; characterization

Received 29 March 1999.


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