Abstract
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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Peyronnet, S., De Rougemont, M., Strozecki, Y. (2012). Approximate Verification and Enumeration Problems. In: Roychoudhury, A., D’Souza, M. (eds) Theoretical Aspects of Computing – ICTAC 2012. ICTAC 2012. Lecture Notes in Computer Science, vol 7521. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32943-2_18
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DOI: https://doi.org/10.1007/978-3-642-32943-2_18
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