Abstract
Immerman and Szelepcsényi's inductive counting technique demonstrated that, for space classes, the nondeterministic acceptance mechanism can simulate with no space penalty any reasonable acceptance mechanism based on censuses of configurations. However, the efficiency with which other acceptance mechanisms can simulate nondeterminism remains an open question. This paper uses inductive counting to study the cost of simulating nondeterminism with Valiant's paradigm of unique computation—nondeterministic computation in which each input generates at most one accepting computation. We show that unique computation can simulate nondeterministic computation with a space penalty logarithmic in the ambiguity of the nondeterministic computation tree. Relatedly, we show that unique AuxPDAs, logspace reductions to unambiguous context-free languages, and PRAMs can efficiently simulate ambiguity-bounded nondeterministic computation. In particular, all nondeterministic logspace languages of polynomial ambiguity are in CREW1, and thus have fast parallel algorithms.
Research supported in part by a Hewlett-Packard Corporation equipment grant and the National Science Foundation under grant CCR-8809174/CCR-8996198 and a Presidential Young Investigator Award.
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References
J. Balcázar, J. Díaz, and J. Gabarró. Structural Complexity I. Springer-Verlag, 1988.
A. Blass and Y. Gurevich. On the unique satisfiability problem. Information and Control, 55:80–88, 1982.
G. Buntrock, L. Hemachandra, and D. Siefkes. Using inductive counting to simulate nondeterministic computation. Technical Report 13, Bayerische Julius Maximilians Universität Würzburg, Würzburg, 1990.
S. Cook. A taxonomy of problems with fast parallel algorithms. Inf. and Control, 64:2–22, 1985.
S. Fortune and J. Wyllie. Parallelism in random access machines. In 10th ACM Symposium on Theory of Computing, pages 114–118, 1978.
L. Goldschlager and I. Parberry. On the construction of parallel computers from various bases of boolean functions. Theoretical Computer Science, 43:43–58, 1986.
N. Immerman. Nondeterministic space is closed under complementation. SIAM Journal on Commputing, 17:935–938, 1988.
R. Karp and V. Ramachandra. Parallel algorithms for sharedmemory machines. In The Handbook of Theoretical Computer Science. To appear.
K.-J. Lange and P. Rossmanith. Characterizing unambiguous augmented pushdown automata by circuits. These Proceedings.
C. Papadimitriou and S. Zachos. Two remarks on the power of counting. In Proceedings 6th GI Conference on Theoretical Computer Science, pages 269–276. Springer-Verlag, 1983.
W. Ruzzo. On uniform circuit complexity. Journal of Computer and System Sciences, 22(3):365–383, 1981.
W. Rytter. Parallel time O(log N) recognition of unambiguous CFLs. In Information and Control, 73:75–86, 1987.
W. Savitch. Relationships between nondeterministic and deterministic tape complexities. Journal of Computer and System Sciences, 4(2):177–192, 1970.
I. Sudborough. On the tape complexity of deterministic contextfree languages. Journal of the ACM, 25:405–414, 1978.
R. Szelepcsényi. The method of forced enumeration for nondeterministic automata. Acta Informatica, 26:279–284, 1988.
A. Szepietowski. Some notes on strong and weak loglogn space complexity. Information Processing Letters, 33(2):109–112, 1989.
L. Valiant. The relative complexity of checking and evaluating. Information Processing Letters, 5:20–23, 1976.
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Buntrock, G., Hemachandra, L.A., Siefkes, D. (1990). Using inductive counting to simulate nondeterministic computation. In: Rovan, B. (eds) Mathematical Foundations of Computer Science 1990. MFCS 1990. Lecture Notes in Computer Science, vol 452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029607
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DOI: https://doi.org/10.1007/BFb0029607
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