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.
Partially supported by NSF grant CCR-9403447, and the John C. Whitehead faculty research fund at Haverford College.
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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.
E. Allender, V. Gore “Rudimentary reductions revisited” Information Processing Letters 40 89–95 (1991).
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.
D. Mix Barrington, K. Compton, H. Straubing, D. Thérien “Regular Languages in NC 1” JCSS, June 1992 pp. 478–499.
D. Mix Barrington, N. Immerman “Time, Hardware, and Uniformity” IEEE Structures, 1994 pp.176–185.
D. Mix Barrington, N. Immerman, H. Straubing “On Uniformity in NC 1” JCSS 41, pp.274–306 (1990).
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.
E. Dahlhaus, “Reduction to NP-complete problems by interpretations” LNCS 171, Springer-Verlag, pp.357–365, 1984.
A. Dawar “Generalized Quantifiers and Logical Reducibilities” Journal of Logic and Computation, Vol 5, No. 2, pp. 213–226, 1995.
H. Enderton, A Mathematical Introduction to Logic, Academic Press, 1972.
M. Furst, J.B. Saxe, M. Sipser “Parity, Circuits, and the Polynomial-time Hierarchy” Math. Syst. Theory 17, pp. 13–27, 1984.
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.
J. W. Hong Computation: Computability, Similarity, and Duality Wiley 1986.
N. Immerman, “Expressibility and Parallel Complexity” SIAM Journal of Computing vol. 18 no. 3, June 1989, pp. 625–638.
N. Immerman, S. Landau “The Complexity of Iterated Multiplication” Information and Computation 116(1):103–116, January 1995.
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.
S. Lindell, The Logical Complexity of Queries on Unordered Graphs, Ph.D. Dissertation, UCLA 1987.
S. Lindell, “A Purely Logical Characterization of Circuit Uniformity” IEEE Structure in Complexity Theory (1992) pp.185–192.
H. Straubing, Finite Automata, Formal Logic, and Circuit Complexity, Birkhäuser, 1994.
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© 1995 Springer-Verlag Berlin Heidelberg
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Lindell, S. (1995). A constant-space sequential model of computation for first-order logic. In: Leivant, D. (eds) Logic and Computational Complexity. LCC 1994. Lecture Notes in Computer Science, vol 960. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60178-3_97
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DOI: https://doi.org/10.1007/3-540-60178-3_97
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