Abstract
We show that any randomized logspace algorithm (running in polynomial time with bounded two-sided error) can be simulated deterministically in polynomial time andO(log2 n) space. This puts RL in SC, “Steve's Class” In particular, we get a polynomial time,O(log2 n) space algorithm for thest-connectivity problem on undirected graphs.Subject classifications. 68Q10, 68Q15, 68Q25.
Similar content being viewed by others
References
R. Aleliunas, R. M. Karp, R. J. Lipton, L. Lovasz, and C. Rackoff, Random walks, universal sequences and the complexity of maze problems. In 20th Annual Symposium on Foundations of Computer Science, San Juan, Puerto Rico, 1979, 218–223.
G. Barnes, and W. L. Ruzzo, Deterministic algorithms for undirecteds-t connectivity using polynomial time and sublinear space. InProceedings of the 23 rd Annual ACM Symposium on Theory of Computing, 1991, 43–53.
A. Borodin, S.A. Cook, P.W. Dymond, W.L. Ruzzo, andM. Tompa, Two applications of inductive counting for complementation problems.SIAM J. Comput. 18(3) (1989), 559–578.
L. Carter andM. Wegman, Universal hash functions.J. Comput. System Sci. 18(2) (1979), 143–154.
N. Nisan, Pseudorandom generators for space-bounded computation.Combinatorica 12(4) (1992), 449–461.
N. Nisan, On read-once vs. multiple access to randomness in logspace.Theoret. Comput. Sci. 107 (1993), 135–144.
W.J. Savitch, Relationships between nondeterministic and deterministic space complexities.J. Comput. System Sci. 4(2) (1970), 177–192.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Nisan, N. RL\( \subseteq \) SC. Comput Complexity 4, 1–11 (1994). https://doi.org/10.1007/BF01205052
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01205052