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Quantitative Model checking

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 and δ, QMC performs random sampling to compute an estimate e pZ of the expectation pZ that the language L(B) of the Buchi 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 e pZ output by QMC is an ( , δ)approximation of pZ—one that is within a factor of 1± 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.