Treffer: Geometrical organization of solutions to random linear Boolean equations

Title:
Geometrical organization of solutions to random linear Boolean equations
Contributors:
Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), MTR 2002-00319 `STIPCO' and FP6 IST consortium `EVERGROW'
Source:
Journal of Statistical Mechanics: Theory and Experiment. :P10007-P10007
Publisher Information:
HAL CCSD; IOP Publishing, 2006.
Publication Year:
2006
Collection:
collection:CNRS
collection:UNIV-PSUD
collection:UNIV-PARIS-SACLAY
collection:UNIV-PSUD-SACLAY
collection:GS-PHYSIQUE
collection:LPTMS
Original Identifier:
ARXIV: cond-mat/0609099
HAL: hal-00091334
Document Type:
Zeitschrift article<br />Journal articles
Language:
English
ISSN:
1742-5468
Relation:
info:eu-repo/semantics/altIdentifier/arxiv/cond-mat/0609099; info:eu-repo/semantics/altIdentifier/doi/10.1088/1742-5468/2006/10/P10007
DOI:
10.1088/1742-5468/2006/10/P10007
Rights:
info:eu-repo/semantics/OpenAccess
Accession Number:
edshal.hal.00091334v1
Database:
HAL

Weitere Informationen

20 pages
The random XORSAT problem deals with large random linear systems of Boolean variables. The difficulty of such problems is controlled by the ratio of number of equations to number of variables. It is known that in some range of values of this parameter, the space of solutions breaks into many disconnected clusters. Here we study precisely the corresponding geometrical organization. In particular, the distribution of distances between these clusters is computed by the cavity method. This allows to study the `x-satisfiability' threshold, the critical density of equations where there exist two solutions at a given distance.