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Characterizations of PUNC and precomputation

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Book cover Automata, Languages and Programming (ICALP 1986)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 226))

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Abstract

Much complexity-theoretic work on parallelism has focused on the class NC, which is defined in terms of logspace-uniform circuits. Yet P-uniform circuit complexity is in some ways a more natural setting for studying feasible parallelism. In this paper, P-uniform NC (PUNC) is characterized in terms of space-bounded AuxPDA's and alternating Turing Machines with bounded access to the input. We also present a general-purpose parallel computer for PUNC; this characterization leads to an easy proof that NC = PUNC iff all tally languages in P are in NC. The characterizations of PUNC lead to natural methods for modelling precomputation. We show that for many classes of interest, there is a single “universal” table which can be used in place of any table of similar size and complexity, while for certain other classes, no such “universal” table exists.

Extended Abstract

Portions of this research were carried out while the author was supported by NSF grant MCS 81-03608.

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References

  1. L. Adleman, Two theorems on random polynomial time, Proc. 19th IEEE Symposium on Foundations of Computer Science, pp. 307–311.

    Google Scholar 

  2. E. W. Allender, Invertible functions, Doctoral Dissertation, Georgia Institute of Technology.

    Google Scholar 

  3. E. W. Allender, The complexity of sparse sets in P, Paper presented at the Structure in Complexity Theory Conference, Berkeley, to appear in Lecture Notes in Computer Science.

    Google Scholar 

  4. J. L. Balcazar, J. Diaz, J. Gabarro, On some “non-uniform” complexity measures, 5th Conference on Mathematical Foundations of Computer Science, Lecture Notes in Computer Science 199, pp. 18–27.

    Google Scholar 

  5. P. W. Beame, S. A. Cook, and H. J. Hoover, Log depth circuits for division and related problems, Proc. 25th IEEE Symposium on Foundations of Computer Science, pp. 1–11.

    Google Scholar 

  6. R. V. Book, Tally languages and complexity classes, Information and Control 26, 186–193.

    Google Scholar 

  7. F.-J. Brandenburg, On one-way auxiliary pushdown automata, Proc. 3rd GI Conference, Lecture Notes in Computer Science 48, pp. 133–144.

    Google Scholar 

  8. F.-J. Brandenburg, The contextsensitivity of contextsensitive grammars and languages, Proc. 4th International Colloquium on Automata, Languages and Programming, Lecture Notes in Computer Science 52, pp. 272–281.

    Google Scholar 

  9. A. K. Chandra, L. J. Stockmeyer, U. Vishkin, Constant depth reducibility, SIAM J. Comput. 13, 423–439.

    Google Scholar 

  10. M. P. Chytil, Comparison of the active visiting and the crossing complexities, Proc. 6th Conference on Mathematical Foundations of Computer Science, Lecture Notes in Computer Science 53, pp. 272–281.

    Google Scholar 

  11. S. A. Cook, Towards a complexity theory of synchronous parallel computation, L'Enseignement Mathematique 27, 99–124.

    Google Scholar 

  12. S. A. Cook, The classification of problems which have fast parallel algorithms. Proc. 4th International Conference on Foundations of Computation Theory, Lecture Notes in Computer Science 158, pp. 78–93.

    Google Scholar 

  13. P. W. Dymond and S. A. Cook, Hardware complexity and parallel computation, Proc. 20th IEEE Symposium on Foundations of Computer Science, pp. 360–372.

    Google Scholar 

  14. J. von zur Gathen, Parallel powering, Proc. 25th Annual ACM Symposium on Theory of Computing, pp. 31–36.

    Google Scholar 

  15. Z. Galil, Some open problems in the theory of computation as questions about two-way deterministic pushdown automaton languages, Mathematical Systems Theory 10, 211–228.

    Google Scholar 

  16. Z. Galil and W. Paul, An efficient general-purpose parallel computer, J. ACM 30, 360–387.

    Google Scholar 

  17. A. V. Goldberg and M. Sipser, Compression and ranking, Proc. 17th Annual ACM Symposium on Theory of Computing, pp. 440–448.

    Google Scholar 

  18. L. M. Goldschlager, A universal interconnection pattern for parallel computers, J. ACM 29, 1073–1086.

    Google Scholar 

  19. J. Hartmanis, Generalized Kolmogorov complexity and the structure of feasible computations, Proc. 24th IEEE Symposium on Foundations of Computer Science, pp. 439–445.

    Google Scholar 

  20. J. Hartmanis and Y. Yesha, Computation times of NP sets of different densities, Theoretical Computer Science 34, 17–32.

    Google Scholar 

  21. D. T. Huynh, Non-uniform complexity and the randomness of certain complete languages, Technical Report TR 85–34, Computer Science Department, Iowa State University.

    Google Scholar 

  22. N. D. Jones, Space-bounded reducibility among combinatorial problems, J. Computer and System Sciences 11, 68–85.

    Google Scholar 

  23. R. M. Karp and R. J. Lipton, Turing machines that take advice, L'Enseignement Mathematique 28, 191–209.

    Google Scholar 

  24. K. N. King, Measures of parallelism in alternating computation trees, Proc. 13th Annual ACM Symposium on Theory of Computing, pp. 189–201.

    Google Scholar 

  25. K.-I. Ko, On the definition of some complexity classes of real numbers, Mathematical Systems Theory 16, 95–109.

    Google Scholar 

  26. K.-I. Ko, A definition of infinite pseudorandom sequences, manuscript, University of Houston.

    Google Scholar 

  27. N. Pippenger, Pebbling with an auxiliary pushdown, J. Computer and System Sciences 23, 151–165.

    Google Scholar 

  28. C. Rackoff, personal communication.

    Google Scholar 

  29. W. L. Ruzzo, On uniform circuit complexity, J. Computer and System Sciences 21, 365–383.

    Google Scholar 

  30. W. L. Ruzzo, personal communication.

    Google Scholar 

  31. L. J. Stockmeyer, The complexity of decision problems in automata theory and logic, Doctoral Dissertation, M.I.T.

    Google Scholar 

  32. I. H. Sudborough, Bandwidth constraints on problems complete for polynomial time, Theoretical Computer Science 26, 25–52.

    Google Scholar 

  33. U. Vishkin, Synchronous parallel computation — a survey, preprint, Courant Institute, New York University.

    Google Scholar 

  34. U. Vishkin, A parallel-design distributed-implementation (PDDI general-purpose computer), Theoretical Computer Science 32, 157–172.

    Google Scholar 

  35. G. Wechsung, The oscillation complexity and a hierarchy of context-free languages, Proc. 2nd Proc. 2nd International Conference on Fundementals of Computation Theory, Akademie-Verlag, Berlin, GDR, pp. 508–515.

    Google Scholar 

  36. G. Wechsung, A note on the return complexity, Elektronische Informationsverarbeitung und Kybernetik 16, 139–146.

    Google Scholar 

  37. G. Wechsung and A. Brandstadt, A relation between space, return and dual return complexities, Theoretical Computer Science 9, 127–140.

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, Rutgers University, 08903, New Brunswick, N.J., USA

    Eric W. Allender

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  1. Eric W. Allender
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Laurent Kott

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© 1986 Springer-Verlag Berlin Heidelberg

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Allender, E.W. (1986). Characterizations of PUNC and precomputation. In: Kott, L. (eds) Automata, Languages and Programming. ICALP 1986. Lecture Notes in Computer Science, vol 226. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16761-7_49

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  • DOI: https://doi.org/10.1007/3-540-16761-7_49

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  • Print ISBN: 978-3-540-16761-7

  • Online ISBN: 978-3-540-39859-2

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