Geometrical organization of solutions to random linear Boolean equations

Details Geometrical organization of solutions to random linear Boolean equations Geometrical organization of solutions to random linear Boolean equations

2006-09-05

arxiv.org/abs/cond-mat/0609099v1

Journal of Statistical Mechanics: Theory and Experiment (2006) P10007

Physics

Condensed Matter

Disordered Systems and Neural Networks

20 pages

Scientific paper

10.1088/1742-5468/2006/10/P10007

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.

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