Efficient detection of vacuity in ACTL formulas
- Cite this paper as:
- Beer I., Ben-David S., Eisner C., Rodeh Y. (1997) Efficient detection of vacuity in ACTL formulas. In: Grumberg O. (eds) Computer Aided Verification. CAV 1997. Lecture Notes in Computer Science, vol 1254. Springer, Berlin, Heidelberg
Prepositional logic formulas containing implications can suffer from antecedent failure, in which the formula is true trivially because the pre-condition of the implication is not satisfiable. In other words, the post-condition of the implication does not affect the truth value of the formula. We call this a vacuous pass, and extend the definition of vacuity to cover other kinds of trivial passes in temporal logic. We define w-ACTL, a subset of CTL and show by construction that for every w-ACTL formula ϕ there is a formula w(ϕ), such that: both ϕ and w(ϕ) are true in some model M iff ϕ passes vacuously. A useful side-effect of w(ϕ) is that if false, any counter-example is also a non-trivial witness of the original formula ϕ.
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