Model Checking and Transitive - Closure Logic ? Neil Immerman ? ?

We give a linear-time algorithm to translate any formula from computation tree logic (CTL or CTL*) into an equivalent expression in a variable-connned fragment of transitive-closure logic FO(TC). Traditionally, CTL and CTL ? have been used to express queries for model checking and then translated into-calculus for symbolic evaluation. Evaluation of-calculus formulas is, however, complete for time polynomial in the (typically huge) number of states in the Kripke structure. Thus, this is often not feasible, not parallelizable, and eecient in-cremental strategies are unlikely to exist. By contrast, evaluation of any formula in FO(TC) requires only NSPACEElog n]. This means that the space requirements are manageable, the entire computation is paralleliz-able, and eecient dynamic evaluation is possible.