The Statistical Mechanics of k-Satisfaction

Scott Kirkpatrick; Géza Györgyi; Naftali Tishby; Lidror Troyansky

The Statistical Mechanics of k-Satisfaction

Scott Kirkpatrick^*
, Géza Györgyi
, Naftali Tishby
, Lidror Troyansky

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

7 Scopus citations

Abstract

The satisfiability of random CNF formulae with precisely k variables per clause ("k-SAT") is a popular testbed for the performance of search algorithms. Formulae have M clauses from N variables, randomly negated, keeping the ratio a = M/N fixed. For k = 2, this model has been proven to have a sharp threshold at α = 1 between formulae which are almost aways satisfiable and formulae which are almost never satisfiable as N → ∞. Computer experiments for k = 2, 3, 4, 5 and 6, (carried out in collaboration with B. Selman of ATT Bell Labs). show similar threshold behavior for each value of k. Finite-size scaling, a theory of the critical point phenomena used in statistical physics, is shown to characterize the size dependence near the threshold. Annealed and replica-based mean field theories give a good account of the results.

Original language	English
Title of host publication	Advances in Neural Information Processing Systems 6, NIPS 1993
Editors	J. Cowan, G. Tesauro, J. Alspector
Publisher	Neural information processing systems foundation
Pages	439-446
Number of pages	8
ISBN (Electronic)	1558603220, 9781558603226
State	Published - 1993
Event	6th Advances in Neural Information Processing Systems, NIPS 1993 - Denver, United States Duration: 29 Nov 1993 → 2 Dec 1993

Publication series

Name	Advances in Neural Information Processing Systems
Volume	6
ISSN (Print)	1049-5258

Conference

Conference	6th Advances in Neural Information Processing Systems, NIPS 1993
Country/Territory	United States
City	Denver
Period	29/11/93 → 2/12/93

Bibliographical note

Publisher Copyright:
© 1993 Neural information processing systems foundation. All rights reserved.

Cite this

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title = "The Statistical Mechanics of k-Satisfaction",

abstract = "The satisfiability of random CNF formulae with precisely k variables per clause ({"}k-SAT{"}) is a popular testbed for the performance of search algorithms. Formulae have M clauses from N variables, randomly negated, keeping the ratio a = M/N fixed. For k = 2, this model has been proven to have a sharp threshold at α = 1 between formulae which are almost aways satisfiable and formulae which are almost never satisfiable as N → ∞. Computer experiments for k = 2, 3, 4, 5 and 6, (carried out in collaboration with B. Selman of ATT Bell Labs). show similar threshold behavior for each value of k. Finite-size scaling, a theory of the critical point phenomena used in statistical physics, is shown to characterize the size dependence near the threshold. Annealed and replica-based mean field theories give a good account of the results.",

author = "Scott Kirkpatrick and G{\'e}za Gy{\"o}rgyi and Naftali Tishby and Lidror Troyansky",

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year = "1993",

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Kirkpatrick, S, Györgyi, G, Tishby, N & Troyansky, L 1993, The Statistical Mechanics of k-Satisfaction. in J Cowan, G Tesauro & J Alspector (eds), Advances in Neural Information Processing Systems 6, NIPS 1993. Advances in Neural Information Processing Systems, vol. 6, Neural information processing systems foundation, pp. 439-446, 6th Advances in Neural Information Processing Systems, NIPS 1993, Denver, United States, 29/11/93.

The Statistical Mechanics of k-Satisfaction. / Kirkpatrick, Scott; Györgyi, Géza; Tishby, Naftali et al.
Advances in Neural Information Processing Systems 6, NIPS 1993. ed. / J. Cowan; G. Tesauro; J. Alspector. Neural information processing systems foundation, 1993. p. 439-446 (Advances in Neural Information Processing Systems; Vol. 6).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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The Statistical Mechanics of k-Satisfaction

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