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

Preliminary draft

Conference paper

First Online:

## 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.

## Preview

Unable to display preview. Download preview PDF.

## References

- [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
- [AG]E. Allender, V. Gore “Rudimentary reductions revisited” Information Processing Letters
**40**89–95 (1991).CrossRefGoogle Scholar - [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 - [BCST]D. Mix Barrington, K. Compton, H. Straubing, D. Thérien “Regular Languages in
*NC*^{1}” JCSS, June 1992 pp. 478–499.Google Scholar - [BI]D. Mix Barrington, N. Immerman “Time, Hardware, and Uniformity” IEEE Structures, 1994 pp.176–185.Google Scholar
- [BIS]D. Mix Barrington, N. Immerman, H. Straubing “On Uniformity in
*NC*^{1}” JCSS**41**, pp.274–306 (1990).Google Scholar - [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 - [D]E. Dahlhaus, “Reduction to NP-complete problems by interpretations” LNCS 171, Springer-Verlag, pp.357–365, 1984.Google Scholar
- [D']A. Dawar “Generalized Quantifiers and Logical Reducibilities” Journal of Logic and Computation, Vol 5, No. 2, pp. 213–226, 1995.Google Scholar
- [E]H. Enderton,
*A Mathematical Introduction to Logic*, Academic Press, 1972.Google Scholar - [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 - [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 - [H]J. W. Hong
*Computation: Computability, Similarity, and Duality*Wiley 1986.Google Scholar - [I]N. Immerman, “Expressibility and Parallel Complexity” SIAM Journal of Computing vol. 18 no. 3, June 1989, pp. 625–638.Google Scholar
- [IL]N. Immerman, S. Landau “The Complexity of Iterated Multiplication” Information and Computation
**116**(1):103–116, January 1995.Google Scholar - [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 - [LI]S. Lindell, The Logical Complexity of Queries on Unordered Graphs, Ph.D. Dissertation, UCLA 1987.Google Scholar
- [L2]S. Lindell, “A Purely Logical Characterization of Circuit Uniformity” IEEE Structure in Complexity Theory (1992) pp.185–192.Google Scholar
- [S]H. Straubing,
*Finite Automata, Formal Logic, and Circuit Complexity*, Birkhäuser, 1994.Google Scholar

## Copyright information

© Springer-Verlag Berlin Heidelberg 1995