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2 claims from 1 paper

1. Computer Science › Constraint Satisfaction and Optimization

   From one solution of a 3-satisfiability formula to a solution cluster: Frozen variables and entropy

   Li, Ma and Zhou · Physical Review E · 2009

   The paper expands single 3-SAT solutions into clusters, studies frozen variables and entropy using whitening and belief propagation, and infers where algorithmic solutions sit among all clusters.

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   1. Unchecked“While frozen cores are identified by a local whitening algorithm, long-range frustrations are very difficult to trace, and they make an entropic belief-propagation (BP) algorithm fail to converge.”
   2. UncheckedFor large random 3-SAT formulas near the satisfiability threshold, survey-propagation and WALKSAT solutions lie in neither the dominating nor the most abundant clusters.“From the calculated entropy values, we infer that, for a large random 3-SAT formula with constraint density close to the satisfiability threshold, the solutions obtained by the survey-propagation or WALKSAT algorithms belong neither to the most dominating clusters of the formula nor to the most abu…”