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A lower bound for the 4-satisfiability threshold
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F. Yu. Vorobyev
Published/Copyright:
June 28, 2007
Let Fk(n, m) be a random k-conjunctive normal form obtained by selecting uniformly and independently m out of all possible k-clauses on n variables. We prove that if F4(n, rn) is unsatisfiable with probability tending to one as n → ∞, then r ≥ 8.09. This sharpens the known lower bound r ≥ 7.91.
Published Online: 2007-06-28
Published in Print: 2007-07-20
Copyright 2007, Walter de Gruyter
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Articles in the same Issue
- The compound Poisson distribution of the number of matches of values of a discrete function of s-tuples in segments of a sequence of random variables
- On stability of an efficient solution of a vector Boolean problem of maximisation of absolute values of linear functions
- Optimal logarithmic functions for lifting of a solution of an exponential congruence
- On the number of independent sets in graphs with fixed independence number
- Homomorphisms and endomorphisms of linear and alinear quasigroups
- On finite groups close to completely factorisable groups
- Non-asymptotic bounds for probabilities of the rank of a random matrix over a finite field
- On representation of k-valued logic functions by a sum of products of subfunctions
- A lower bound for the 4-satisfiability threshold
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