STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Algorithmic derandomization via complexity theory
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Universal traversal sequences with backtracking
Journal of Computer and System Sciences - Complexity 2001
On the Derandomization of Space-Bounded Computations
RANDOM '98 Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science
Modeling and analyzing social network dynamics using stochastic discrete graphical dynamical systems
Theoretical Computer Science
| Hi-index | 0.00 |
We prove that any language that can be recognized by a randomized algorithm (with possibly two-sided error) that runs in space S and expected time 2^0(s) can be recognized by a deterministic algorithm running in space S^3/2. This improves over the best previously known result that such algorithms have deterministic space S^2 simulations which, for one-sided error algorithms, follows from Savitch's Theorem and for two-sided error algorithms follows by reduction to recursive matrix powering. Our result includes as a special case the result due to N. Nisan et al., that undirected connectivity can be computed in space log^3/2 n. It is obtained via a new algorithm for repeated squaring of a matrix we show how to approximate the 2r power of a d x d matrix in space r^1/2 log d, improving on the bound of r log d that comes from the natural recursive algorithm. The algorithm employs Nisan's pseudorandom generator for space bounded computation, together with some new techniques for reducing the number of random bits needed by an algorithm.