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FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
A resolution calculus for the branching-time temporal logic CTL
ACM Transactions on Computational Logic (TOCL)
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In this paper, we present a resolution-based calculus R CTL ,S for Computation Tree Logic (CTL) as well as an implementation of that calculus in the theorem prover CTL-RP. The calculus R CTL ,S requires a transformation of an arbitrary CTL formula to an equi-satisfiable clausal normal form formulated in an extension of CTL with indexed path formulae. The calculus itself consists of a set of resolution rules which can be used for an EXPTIME decision procedure for the satisfiability problem of CTL. We give a formal semantics for the clausal normal form, provide proof sketches for the soundness and completeness of the resolution rules, discuss the complexity of the decision procedure based on R CTL ,S, and present an approach to implementing the calculus R CTL ,S using first-order techniques. Finally, we give a comparison between CTL-RP and a tableau theorem prover for CTL.