Abstract
We present a deterministic algorithm running in space O (log2 n/log log n) solving the connectivity problem on strongly unambiguous graphs. In addition, we present an O(log n) time-bounded algorithm for this problem running on a parallel pointer machine.
Supported in part by NSF grant CCR-9509603.
Supported in part by NSF grant CCR-9509603.
Preview
Unable to display preview. Download preview PDF.
References
R. J. Anderson and G. L. Miller. Deterministic parallel list ranking. In VLSI Algorithms and Architectures, Proc. 3rd Aegean Workshop on Computing, number 319 in LNCS, pages 81–90. Springer, 1988.
A. Blass and Y. Gurevich. On the unique satisfiability problem. Inform. and Control, 55:80–88, 1982.
G. Buntrock, B. Jenner, K.-J. Lange, and P. Rossmanith. Unambiguity and fewness for logarithmic space. In Proc. of the 8th Conference on Fundamentals of Computation Theory, number 529 in LNCS, pages 168–179, 1991.
R. Cole and U. Vishkin. Approximate parallel scheduling, part i: the basic technique with applications to optimal parallel list ranking in logarithmic time. SIAM J. Comp., 17:128–142, 1988.
S. Cook. Deterministic CFL's are accepted simultaneously in polynomial time and log squared space. In Proc. of the 11th Annual ACM Symp. on Theory of Computing, pages 338–345, 1979.
S. Cook and P. Dymond. Parallel pointer machines. Computational Complexity, 3:19–30, 1993.
P. Dymond and W. Ruzzo. Parallel RAMs with owned global memory and deterministic context-free language recoginition. In Proc. of 13th International Colloquium on Automata, Languages and Programming, number 226 in LNCS, pages 95–104. Springer, 1986.
M. Fellows and N. Koblitz. Self-witnessing polynomial-time complexity and prime factorization. In Proc. of the 7th IEEE Structure in Complexity Conference, pages 107–110, 1992.
H. Fernau, K.-J. Lange, and K. Reinhardt. Advocating ownership. In Proc. of the 17th FST&TCS, 1996. to be published.
J. Hopcroft and J. Ullman. Introduction to Automata Theory, Language, and Computation. Addison-Wesley, Reading Mass., 1979.
N. Immerman. Nondeterministic space is closed under complementation. SIAM J. Comp., 17:935–938, 1988.
M. Karchmer and A. Wigderson. On span programs. In Proc. of the 8th IEEE Structure in Complexity Theory Conference, pages 102–111, 1993.
R.M. Karp and V. Ramachandran. A Survey of Parallel Algorithms for Shared-Memory Machines. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, Vol. A, pages 869–941. Elsevier, Amsterdam, 1990.
T. Lam and W. Ruzzo. The power of parallel pointer manipulation. In Proc. of the 1st ACM Symposium on Parallel Algorithms and Architectures (SPAA'89), pages 92–102, 1989.
K.-J. Lange. An unambiguous class possessing a complete set. Manuscript, 1996.
K.-J. Lange and R. Niedermeier. Data-independences of parallel random access machines. In Proc. of 13th Conference on Foundations of Software Technology and Theoretical Computer Science, number 761 in LNCS, pages 104–113. Springer, 1993.
B. Monien, W. Rytter, and H. Schäpers. Fast recognition of deterministic cfl's with a smaller number of processors. Theoret. Comput. Sci., 116:421–429, 1993. Corrigendum, 123:427,1993.
N. Nisan. RL ⊂-SC. In Proc. of the 24th Annual ACM Symposium on Theory of Computing, pages 619–623, 1992.
N. Nisan, E. Szemeredi, and A. Wigderson. Undirected connectivity in O(log1.5 n) space. In Proc. of 33th Annual IEEE Symposium on Foundations of Computer Science, pages 24–29, 1992.
P. Rossmanith. The owner concept for PRAMs. In Proc. of the 8th STACS, number 480 in LNCS, pages 172–183. Springer, 1991.
I. Sudborough. On the tape complexity of deterministic context-free languages. J. Assoc. Comp. Mach., 25:405–414, 1978.
R. Szelepcsényi. The method of forcing for nondeterministic automata. Acta Informatica, 26:279–284, 1988.
A. Wigderson. NL/poly ⊂-⊕ L/poly. In Proc. of the 9th IEEE Structure in Complexity Theory Conference, pages 59–62, 1994.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Allender, E., Lange, KJ. (1996). StUSPACE(log n) ⊂-DSPACE(log2 n/log log n). In: Asano, T., Igarashi, Y., Nagamochi, H., Miyano, S., Suri, S. (eds) Algorithms and Computation. ISAAC 1996. Lecture Notes in Computer Science, vol 1178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0009495
Download citation
DOI: https://doi.org/10.1007/BFb0009495
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-62048-8
Online ISBN: 978-3-540-49633-5
eBook Packages: Springer Book Archive