We study enumeration problems using probabilistic methods, with application to verification problems. We consider the enumeration of monomials of a polynomial given as a black box, and the enumeration of discrete points which separate two polytopes in a space of dimension n, using a random walk which provides witnesses if the volume of the difference of the polytopes is large enough. The first method allows to enumerate all words of a given size which distinguish two probabilistic automata with a polynomial delay. The second method enumerates words which ε-distinguish two nondeterministic finite automata. We also enumerate strategies which ε-distinguish two Markov Decision Processes in time polynomial in the dimension of their statistical representation.
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