An Experimental Comparison of Theorem Provers for CTL

Abstract

We compare implementations of five theorem provers for Computation Tree Logic (CTL) based on treetableaux, graph-tableaux, binary decision diagrams, resolution and games using formula-classes from the literature. In the process, we gather and analyse a set of test formulae which could form the basis of a suite of benchmark formulae for CTL.

A resolution calculus for the branching-time temporal logic CTL

“…Each of these is discussed more fully in Section 7. Goré et al [2011] conclude that no one prover is the best for all problems and that each prover has problems where it performed badly. Additionally, they state that CTL-RP (and BDDCTL) are "more robust than the tableaux methods since they tend to succeed eventually rather than fail spectacularly or succeed spectacularly".…”

“…In Goré et al [2011], a comparison of five CTL provers, including CTL-RP, is carried out. The provers compared are CTL-RP, BDDCTL [Marrero 2005], MLSolver [Friedmann and Lange 2009], GMUL [Ben-Ari et al 1981], and TreeTab [Abate et al 2007].…”

“…This has been implemented and run on a number of examples. However, Goré et al [2011] notes flaws in the implementation and the prover does not seem to be publicly available.…”

“…UB is a sublogic of CTL which does not contain the operators A U and E U . Goré et al [2011] have implemented this tableau algorithm, extended to allow for until operators as part of their evaluation of CTL provers. Attie [2003] is primarily interested in synthesising a concurrent program from a specification.…”

“…However, the aim of TWB was extensibility rather than efficiency. An optimised version of the one-pass tableau, called TreeTab, has also been implemented and used as part of the comparisons in Goré et al [2011].…”