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Journal of Logic and Computation 1992 2(2):173-210; doi:10.1093/logcom/2.2.173
© 1992 by Oxford University Press
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Original Articles

Efficient Temporal Satisfiability1

E. ALLEN EMERSON*,{dagger}, TOM SADLER* and JAI SRINIVASAN{ddagger}

*Department of Computer Sciences, The Uinversity of Texas at Austin USA
{dagger}Mathematics and Computing Science Department, Eindhoven University of Technology The Netherlands
{ddagger}Dowell Schlumberger. Tulsa OK, USA

There has been much interest in decision procedures for testing satisfiability in various systems of temporal logic. This is due to the potential applications of these decision procedures to reasoning about the correctness of concurrent programs. In this paper, we exhibit a temporal logic that is both useful in applications to program reasoning and is efficiently decidable in quadratic time. A surprising corollary of our results is that the fragment of CTL (Computation Tree Logic) used by Emerson & Clarke [11] to synthesize concurrent programs from temporal specifications is actually decidable in polynomial time. Our results demonstrate that many useful correctness properties can be expressed with a rather restricted syntax, and provide insight into the relation between the syntactic complexity of temporal logics and the complexity of testing satisfiability.


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