# Symmertric space-bounded computation (extended abstract)

Conference paper

First Online:

## Abstract

A symmetric Turing machine is one whose "yields" relation between configurations is symmetric. The space complexity classes for such machines are found to be intermediate between the corresponding deterministic and nondeterministic space complexity classes. Certain natural problems are shown to be complete for symmetric space complexity classes, and the relationship of symmetry to determinism and nondeterminism is investigated.

## Keywords

Turing Machine Logarithmic Space Pushdown Automaton Tape Head Thue System
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Preview

Unable to display preview. Download preview PDF.

## References

- [AKLLR]R. Aleliunas, R.M. Karp, R.J. Lipton, L. Lovasz, C. Rackoff: Random walks, universal sequences, and the complexity of maze problems, Proceedings of 20th Annual Symposium on Foundations of Computer Science, 1979, pp. 218–223.Google Scholar
- [Co]S.A. Cook: Characterizations of pushdown machines in terms of time-bounded computers, Journal of the Association for Computing Machinery 18 (1971), pp. 4–18.Google Scholar
- [Cy]A. Cypher: An approach to the k-paths problem, Proceedings of 12th Annual Symposium on Theory of Computing, 1980.Google Scholar
- [FHW]S. Fortune, J.E. Hopcroft, J. Wyllis: The directed subgraph homeomorphism problem, Theoretical Computer Science 10 (1980), pp. 111–121.Google Scholar
- [Gi]J. Gill: Computational complexity of probabilistic Turing machines, SIAM Journal on Computing 6 (1977), pp. 675–695.Google Scholar
- [HU1]J.D. Hopcroft, J.E. Ullman: Nonerasing stack automata, Journal of the Association for Computing Machinery 18 (1971), pp. 4–18.Google Scholar
- [HU2]J.D. Hopcroft, J.E. Ullman:
*Introduction to Automata Theory, Languages, and Computation*, Addison-Wesley, 1979.Google Scholar - [Ji]H. Jia-wei: On some deterministic space complexity problems, Proceedings of 12th Annual Symposium on Theory of Computing, 1980.Google Scholar
- [Jo]N.D. Jones: Space-bounded reducibility among combinatorial problems, Journal of Computer and Systems Sciences 11 (1972), pp. 68–85.Google Scholar
- [JoLL]N.D. Jones, Y.E. Lien, W.T. Laaser: New problems complete for log space, Mathematical Systems Theory 10 (1976), pp. 1–17.Google Scholar
- [LaP]A. LaPaugh: Private communication, November 1979.Google Scholar
- [LaPR]A. LaPaugh, R.L. Rivest: The subgraph homeomorphism problem, Proceedings of 10th Annual Symposium on Theory of Computing, 1978, pp. 40–50.Google Scholar
- [LP]H.R. Lewis, C.H. Papadimitriou:
*Elements of the Theory of Computation*, Prentice-Hall, 1981 (to appear).Google Scholar - [Po]E.L. Post: Recursive unsolvability of a problem of Thue, Journal of Symbolic Logic 13 (1947), pp. 1–11.Google Scholar
- [RF]S. Ruby and P.C. Fischer: Translational methods and computational complexity, IEEE Conference Record on Switching Circuit Theory and Logical Design, 1965, pp. 173–178.Google Scholar
- [Sa]W.J. Savitch: Relations between nondeterministic and deterministic tape complexities, Journal of Computer and Systems Sciences 4 (1970), pp. 177–192.Google Scholar
- [Sh]Y. Shiloach: The two paths problem is polynomial, Journal of the Association for Computing Machinery, to appear.Google Scholar
- [SaS]W.J. Sakoda, M. Sipser: Nondeterminism and the size of two-way finite automata, Proceedings of 10th Annual Symposium on Theory of Computing, 1978, pp. 275–286.Google Scholar
- [Si]M. Sipser: Lower bounds on the size of sweeping automata, Proceedings of 11th Annual Symposium on Theory of Computing, 1979, pp. 360–364.Google Scholar

## Copyright information

© Springer-Verlag Berlin Heidelberg 1980