Generating functions and the satisfiability threshold - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2004

Generating functions and the satisfiability threshold

Vincent Puyhaubert
  • Function : Author

Abstract

The 3-SAT problem consists in determining if a boolean formula with 3 literals per clause is satisfiable. When the ratio between the number of clauses and the number of variables increases, a threshold phenomenon is observed: the probability of satisfiability appears to decrease sharply from 1 to 0 in the neighbourghood of a threshold value, conjectured to be close to 4.25. Although the threshold has been proved to exist for the 2-SAT formulæ and for closely related problems like 3-XORSAT, there is still no proof for the 3-sat problem. Recent works have provided so far upper and lower bounds for the threshold's potential location. We present here a unified approach to upper bounds that is based on urn models, generating functions, and saddle-point bounds. In this way, we re-derive some of the most significant upper bounds known in a simple and uniform manner.
Fichier principal
Vignette du fichier
dm060216.pdf (101.66 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00959018 , version 1 (13-03-2014)

Identifiers

Cite

Vincent Puyhaubert. Generating functions and the satisfiability threshold. Discrete Mathematics and Theoretical Computer Science, 2004, Vol. 6 no. 2 (2), pp.425-436. ⟨10.46298/dmtcs.325⟩. ⟨hal-00959018⟩
112 View
634 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More