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Status: Unchecked ×Keyword: critical exponents ×Clear all

3 claims from 1 paper

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

   The paper determines how sharply random 2-SAT formulas switch from almost surely satisfiable to almost surely unsatisfiable, and proves the transition is continuous with exponents matching the random graph.

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   1. UncheckedFor random 2-SAT, the transition from satisfiable to unsatisfiable happens in a window of width of order n^(-1/3) around a clause-to-variable ratio of 1.“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. UncheckedThe paper proves that the random 2-SAT phase transition is continuous, with an order parameter critical exponent equal to 1.“Using this order parameter, we prove that the 2-SAT phase transition is continuous with an order parameter critical exponent of 1.”
   3. UncheckedThe paper determines two further critical exponents for random 2-SAT and reports that its exponents match those of the random graph.“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.”