Quantitative Model checking.
Radu Grosu, Scott A. Smolka · 2004
Abstract. We present QMC, a one-sided error Monte Carlo decision procedure for the LTL model-checking problem S | = ϕ. Besides serving as a randomized algorithm for LTL model checking, QMC delivers quantitative information about the likelihood that S | = ϕ. In particular, given a specification S of a finite-state system, an LTL formula ϕ, and parameters ɛ and δ, QMC performs random sampling to compute an estimate epZ of the expectation pZ that the language L(B) oftheBüchi automaton B = BS × B¬ϕ is empty; B is such that L(B) = ∅ iff S | = ϕ. A random sample in our case is a lasso, i.e. an initialized random walk through B ending in a cycle. The estimate epZ output by QMC is an (ɛ, δ)approximation of pZ—one that is within a factor of 1±ɛ with probability at least 1−δ—and is computed using a number of samples N that is optimal to within a constant factor, in expected time O(N · D) and expected space O(D), where D is B’s recurrence diameter. Experimental results demonstrate that QMC is fast, memory-efficient, and scales extremely well. 1