Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
Simple local search problems that are hard to solve
SIAM Journal on Computing
On the Size of Weights for Threshold Gates
SIAM Journal on Discrete Mathematics
Simple strategies for large zero-sum games with applications to complexity theory
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Anti-Hadamard matrices, coin weighing, threshold gates, and indecomposable hypergraphs
Journal of Combinatorial Theory Series A
Concrete Mathematics: A Foundation for Computer Science
Concrete Mathematics: A Foundation for Computer Science
Structure in locally optimal solutions
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Problems of Information Transmission
Winning Concurrent Reachability Games Requires Doubly-Exponential Patience
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
Weights of exact threshold functions
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Exact algorithms for solving stochastic games: extended abstract
Proceedings of the forty-third annual ACM symposium on Theory of computing
The complexity of solving reachability games using value and strategy iteration
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
On the Hardness of Decoding the Gale–Berlekamp Code
IEEE Transactions on Information Theory
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For matrix games we study how small nonzero probability must be used in optimal strategies. We show that for nxn win-lose-draw games (i.e. (-1,0,1) matrix games) nonzero probabilities smaller than n^-^O^(^n^) are never needed. We also construct an explicit nxn win-lose game such that the unique optimal strategy uses a nonzero probability as small as n^-^@W^(^n^). This is done by constructing an explicit (-1,1) nonsingular nxn matrix, for which the inverse has only nonnegative entries and where some of the entries are of value n^@W^(^n^).