%0 Journal Article
%T Pairs of SAT Assignment in Random Boolean Formulae
%+ Laboratoire d'Analyse, Topologie, Probabilités (LATP)
%+ Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
%+ Politecnico di Torino = Polytechnic of Turin (Polito)
%A Daudé, Hervé
%A Mezard, Marc
%A Mora, Thierry
%A Zecchina, Riccardo
%Z MTR 2002-00319 'STIPCO' & FP6 IST consortium 'EVERGROW'
%< avec comité de lecture
%@ 1879-2294
%J Theoretical Computer Science
%I Elsevier
%V 393
%P 260-279
%8 2008-03-20
%D 2008
%Z cond-mat/0506053
%R 10.1016/j.tcs.2008.01.005
%K satisfiability
%K clustering
%Z PACS: 75.10.Nr, 75.40.-s, 75.40.Mg
%Z Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn]
%Z Computer Science [cs]/Computational Complexity [cs.CC]Journal articles
%X We investigate geometrical properties of the random K-satisfiability problem using the notion of x-satisfiability: a formula is x-satisfiable if there exist two SAT assignments differing in Nx variables. We show the existence of a sharp threshold for this property as a function of the clause density. For large enough K, we prove that there exists a region of clause density, below the satisfiability threshold, where the landscape of Hamming distances between SAT assignments experiences a gap: pairs of SAT-assignments exist at small x, and around x=1/2, but they donot exist at intermediate values of x. This result is consistent with the clustering scenario which is at the heart of the recent heuristic analysis of satisfiability using statistical physics analysis (the cavity method), and its algorithmic counterpart (the survey propagation algorithm). The method uses elementary probabilistic arguments (first and second moment methods), and might be useful in other problems of computational and physical interest where similar phenomena appear.
%G English
%2 https://hal.science/hal-00005109v3/document
%2 https://hal.science/hal-00005109v3/file/clustertcs7.pdf
%L hal-00005109
%U https://hal.science/hal-00005109
%~ LATP
%~ CNRS
%~ UNIV-AMU
%~ UNIV-PSUD
%~ I2M
%~ UNIV-PARIS-SACLAY
%~ UNIV-PSUD-SACLAY
%~ GS-PHYSIQUE
%~ LPTMS