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1,167 claims from 736 papers are on the record. 43 have been checked so far; the other 1,124 have no check with a result yet.

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Status: Unchecked ×Keyword: 2-SAT ×Clear all

6 claims from 3 papers

1. Computer Science › Constraint Satisfaction and Optimization

   The scaling window of the 2‐SAT transition

   Bollobás, Borgs, Chayes, Kim and Wilson · Random Structures and Algorithms · 2001

   Unchecked3 claims
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   1. Unchecked“We show that W(n,delta)=(1-Theta(n^{-1/3}),1+Theta(n^{-1/3})), where the constants implicit in Theta depend on delta.”
   2. Unchecked“Using this order parameter, we prove that the 2-SAT phase transition is continuous with an order parameter critical exponent of 1.”
   3. Unchecked“We also determine the values of two other critical exponents, showing that the exponents of 2-SAT are identical to those of the random graph.”

2. Computer Science › Constraint Satisfaction and Optimization

   The number of satisfying assignments of random 2‐SAT formulas

   Achlioptas, Coja‐Oghlan, Hahn‐Klimroth et al. · Random Structures and Algorithms · 2021

   Unchecked2 claims
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   1. Unchecked“The proof is based on showing that the Belief Propagation algorithm renders the correct marginal probability that a variable is set to `true' under a uniformly random satisfying assignment.”
   2. Unchecked“We show that throughout the satisfiable phase the normalised number of satisfying assignments of a random $2$-SAT formula converges in probability to an expression predicted by the cavity method from statistical physics.”

3. Computer Science › Constraint Satisfaction and Optimization

   Phase transitions of the typical algorithmic complexity of the random satisfiability problem studied with linear programming

   Schawe, Bleim and Hartmann · PLoS ONE · 2019

   Unchecked1 claim
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   1. Unchecked“For the present random $K$-SAT problem we have investigated numerous structural properties also exhibiting clear transitions, but they appear not be correlated to the here observed easy-hard transitions.”