A polynomial-time algorithm for the equivalence of probabilistic automata
SIAM Journal on Computing
Random walks and an O*(n5) volume algorithm for convex bodies
Random Structures & Algorithms
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
Randomness efficient identity testing of multivariate polynomials
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Markov Decision Processes: Discrete Stochastic Dynamic Programming
The string edit distance matching problem with moves
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Finite State Markovian Decision Processes
Finite State Markovian Decision Processes
Probabilistic algorithms for sparse polynomials
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Polynomial Time Algorithms for Testing Probabilistic Bisimulation and Simulation
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
On the Resemblance and Containment of Documents
SEQUENCES '97 Proceedings of the Compression and Complexity of Sequences 1997
Metrics for labelled Markov processes
Theoretical Computer Science - Logic, semantics and theory of programming
Blocking Conductance and Mixing in Random Walks
Combinatorics, Probability and Computing
Statistic Analysis for Probabilistic Processes
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
Enumeration of the monomials of a polynomial and related complexity classes
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Approximate Satisfiability and Equivalence
SIAM Journal on Computing
Language equivalence for probabilistic automata
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
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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.