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A constant-space sequential model of computation for first-order logic

Preliminary draft
  • Steven Lindell
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 960)

Abstract

We define and justify a natural sequential model of computation with a constant amount of read/write work space, despite unlimited (polynomial) access to read-only input and write-only output. The model is both deterministic, uniform, and sequential. The constant work space is modeled by a finite number of destructive read boolean variables, assignable by formulas over the canonical boolean operations. We then show that computation on this model is equivalent to expressibility in first-order logic, giving a duality between (read-once) constant-space serial algorithms and constant-time parallel algorithms.

Keywords

Dependency Graph Binary String Regular Language Boolean Variable Finite Automaton 
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.

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References

  1. [ABI]
    E. Allender, Balcázar, N.. Immerman “A First-Order Isomorphism Theorem” to appear in SIAM Journal on Computing. A preliminary version appeared in Proc. 10th Symposium on Theoretical Aspects of Computer Science, Springer-Verlag LNCS 665, pp. 163–174, 1993.Google Scholar
  2. [AG]
    E. Allender, V. Gore “Rudimentary reductions revisited” Information Processing Letters 40 89–95 (1991).CrossRefGoogle Scholar
  3. [B]
    S. Buss, “Algorithms for Boolean Formula Evaluation and for Tree Contraction” in Arithmetic, Proof Theory, and Computational Complexity, editors: Peter Clote and Jan Krajícěk, Oxford University Press, pp.95–115, 1993.Google Scholar
  4. [BCST]
    D. Mix Barrington, K. Compton, H. Straubing, D. Thérien “Regular Languages in NC 1” JCSS, June 1992 pp. 478–499.Google Scholar
  5. [BI]
    D. Mix Barrington, N. Immerman “Time, Hardware, and Uniformity” IEEE Structures, 1994 pp.176–185.Google Scholar
  6. [BIS]
    D. Mix Barrington, N. Immerman, H. Straubing “On Uniformity in NC 1” JCSS 41, pp.274–306 (1990).Google Scholar
  7. [C]
    P. Clote “Sequential, machine-independent characterizations of the parallel complexity classes AlogTIME, AC k, NC k and NC.” in Feasible Mathematics, S. Buss and P. Scott editors, Birkhäuser 1990.Google Scholar
  8. [D]
    E. Dahlhaus, “Reduction to NP-complete problems by interpretations” LNCS 171, Springer-Verlag, pp.357–365, 1984.Google Scholar
  9. [D']
    A. Dawar “Generalized Quantifiers and Logical Reducibilities” Journal of Logic and Computation, Vol 5, No. 2, pp. 213–226, 1995.Google Scholar
  10. [E]
    H. Enderton, A Mathematical Introduction to Logic, Academic Press, 1972.Google Scholar
  11. [FSS]
    M. Furst, J.B. Saxe, M. Sipser “Parity, Circuits, and the Polynomial-time Hierarchy” Math. Syst. Theory 17, pp. 13–27, 1984.Google Scholar
  12. [G]
    Y. Gurevich “Logic and the Challenge of Computer Science” in Trends in Theoretical Computer Science, Editor: Egon Börger, Computer Science Press, 1988, pp.1–57.Google Scholar
  13. [H]
    J. W. Hong Computation: Computability, Similarity, and Duality Wiley 1986.Google Scholar
  14. [I]
    N. Immerman, “Expressibility and Parallel Complexity” SIAM Journal of Computing vol. 18 no. 3, June 1989, pp. 625–638.Google Scholar
  15. [IL]
    N. Immerman, S. Landau “The Complexity of Iterated Multiplication” Information and Computation 116(1):103–116, January 1995.Google Scholar
  16. [IZ]
    S. Istrail, D. Zivkovic “Bounded-width polynomial-size Boolean formulas compute exactly those functions in AC O” Information Processing Letters 50, pp.211–216, 1994.Google Scholar
  17. [LI]
    S. Lindell, The Logical Complexity of Queries on Unordered Graphs, Ph.D. Dissertation, UCLA 1987.Google Scholar
  18. [L2]
    S. Lindell, “A Purely Logical Characterization of Circuit Uniformity” IEEE Structure in Complexity Theory (1992) pp.185–192.Google Scholar
  19. [S]
    H. Straubing, Finite Automata, Formal Logic, and Circuit Complexity, Birkhäuser, 1994.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Steven Lindell
    • 1
  1. 1.Department of Computer ScienceHaverford CollegeHaverford

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