How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
Approximate counting, uniform generation and rapidly mixing Markov chains
Information and Computation
Journal of Computer and System Sciences
On recycling the randomness of states in space bounded computation
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Journal of Computer and System Sciences - Special issue on the 36th IEEE symposium on the foundations of computer science
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Algorithmic derandomization via complexity theory
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
In search of an easy witness: exponential time vs. probabilistic polynomial time
Journal of Computer and System Sciences - Complexity 2001
Stable distributions, pseudorandom generators, embeddings and data stream computation
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
An O(log n log log n) space algorithm for undirected st-connectivity
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Derandomizing polynomial identity tests means proving circuit lower bounds
Computational Complexity
Pseudorandom walks on regular digraphs and the RL vs. L problem
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
S-T Connectivity on Digraphs with a Known Stationary Distribution
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Random walks, universal traversal sequences, and the complexity of maze problems
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Undirected connectivity in log-space
Journal of the ACM (JACM)
Conductance and convergence of Markov chains-a combinatorial treatment of expanders
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Derandomized constructions of k-wise (almost) independent permutations
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
On the power of the randomized iterate
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
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We present a deterministic logspace algorithm for solving S-T Connectivity on directed graphs if: (i) we are given a stationary distribution of the random walk on the graph in which both of the input vertices s and t have nonnegligible probability mass and (ii) the random walk which starts at the source vertex s has polynomial mixing time. This result generalizes the recent deterministic logspace algorithm for S-T Connectivity on undirected graphs [Reingold, 2008]. It identifies knowledge of the stationary distribution as the gap between the S-T Connectivity problems we know how to solve in logspace (L) and those that capture all of randomized logspace (RL).