decision procedures and expressiveness in the temporal logic of branching time
In this paper we consider the Computation Tree Logic (CTL) proposed in [CE] which extends the Unified Branching Time Logic (UB) of [BMP] by adding an until operator. We establish that CTL has the small property by showing that any satisfiable CTL formulae is satisfiable in a small finite model obtained from a small -&-ldquo;pseudo-model-&-rdquo; resulting from the Fischer Ladner quotient construction. We then give an exponential time algorithm for deciding satisfiability in CTL, and extend the axiomatization of UB given in [BMP] to a complete axiomatization for CTL. Lastly, we study the relative expressive power of a family of temporal logics obtained by extending or restricting the syntax of UB and CTL.
decision procedures express temporal temporal logic logic timing paper computation tree operability satisfiability model algorithm completeness power families relation