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A Note on Nondeterminism in Small, Fast Parallel Computers
May 1989 (vol. 38 no. 5)
pp. 766-767
Nondeterministic analogues of the well-known language classes NC and SC called NNC and NSC, respectively, are investigated. NC is the class of languages that can be accepted by small, fast parallel computers; SC is the class of languages that can be recognized by a deterministic Turing machine in polynomial time and polylog tape-head reversals. Adding nondeterminism to SC leaves it in the domai

[1] A. V. Aho, J. E. Hopcroft, and J. D. Ullman,The Design and Analysis of Computer Algorithms. Menlo Park, CA: Addison-Wesley, 1974.
[2] S. A. Cook, "The complexity of theorem-proving procedures," inProc. 3rd Annu. ACM Symp. Theory of Comput., 1971, pp. 151-158.
[3] S. A. Cook, "Towards a complexity theory of synchronous parallel computation,"L'Enseignement Mathematique, vol. 30, 1980.
[4] P. W. Dymond, "Simultaneous resource bounds and parallel computations," Ph.D. dissertation, Tech. Rep. TR145/80, Dep. Comput. Sci., Univ. of Toronto, Aug. 1980.
[5] P. W. Dymond and S. A. Cook, "Hardware complexity and parallel computation," inProc. 21st Annu. IEEE Symp. Foundations Comput. Sci., Oct. 1980, pp. 360-372.
[6] M. R. Garey and D. S. Johnson,Computers and Intractability: A Guide to Theory of NP-Completeness. San Francisco, CA: Freeman, 1979.
[7] L. M. Goldschlager, "Synchronous parallel computation," Ph.D. dissertation, Tech. Rep. TR-114, Dep. Comput. Science, Univ. of Toronto, Dec. 1977.
[8] L. M. Goldschlager, "ε-productions in context-free grammars,"Acta Informatica, vol. 16, no. 3, pp. 303-308, 1981.
[9] L. M. Goldschlager, "A universal interconnection pattern for parallel computers,"J. ACM, vol. 29, pp. 1073-1086, Oct. 1982.
[10] L. M. Goldschlager and I. Parberry, "On the construction of parallel computers from various bases of Boolean functions,"Theor. Comput. Sci., vol. 43, pp. 43-48, May 1986.
[11] L. M. Goldschlager, R. A. Shaw, and J. Staples, "The maximum flow problem is log space complete forP," Theor. Comput. Sci., vol. 21, no. 1, pp. 105-111, 1982.
[12] J.E. Hopcroft and J.D. Ullman,Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, Reading, Mass., 1979.
[13] R. M. Karp, "Reducibility among combinatorial problems," inComplexity of Computer Computations, J. W. Thatcher, Ed. New York: Plenum, 1972.
[14] R. E. Ladner, "The circuit value problem is log space complete for P,"SIGACT News, vol. 7, no. 1, pp. 18-20, 1975.
[15] I. Parberry, "A complexity theory of parallel computation," Ph.D. dissertation, Dep. Comput. Sci., Univ. of Warwick, May 1984.
[16] I. Parberry, "Some practical simulations of impractical parallel computers," inVLSI: Algorithms and Architectures, P. Bertollazzi and F. Lucio, Eds. inProc. Int. Workshop Parallel Comput. VLSI, North-Holland, 1985, pp. 27-37.
[17] I. Parberry, "An improved simulation of space and reversal bounded deterministic Turing machines by width and depth bounded uniform circuits,"Inform. Proc. Lett., vol. 24, pp. 363-367, Apr. 1987.
[18] I. Parberry,Parallel Complexity Theory, Research Notes in Theoretical Computer Science. London, England: Pitman, 1987.
[19] N. Pippenger, "On simultaneous resource bounds," inProc. 20th Annu. IEEE Symp. Foundations Comput. Sci., Oct. 1979, pp. 307- 311.
[20] W. L. Ruzzo, "On uniform circuit complexity,"J. Comput. Syst. Sci., vol. 22, pp. 365-383, June 1981.
[21] W. J. Savitch, "Relationships between nondeterministic and deterministic tape complexities,"J. Comput. Syst. Sci., vol. 4, no. 2, pp. 177-192, 1970.

Index Terms:
nondeterministic analogues; nondeterminism; fast parallel computers; language classes; NC; SC; NNC; NSC; deterministic Turing machine; polylog tape-head reversals; parallel computation; POLYLOGSPACE; subset; simultaneous polynomial time; read-only input tape; read-write work tape; computational complexity; formal languages; parallel machines; Turing machines.
I. Parberry, "A Note on Nondeterminism in Small, Fast Parallel Computers," IEEE Transactions on Computers, vol. 38, no. 5, pp. 766-767, May 1989, doi:10.1109/12.24282
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