• Corpus ID: 15173394

Concentration of the number of solutions of random planted CSPs and Goldreich's one-way candidates

  title={Concentration of the number of solutions of random planted CSPs and Goldreich's one-way candidates},
  author={Emmanuel Abbe and Katherine Edwards},
This paper shows that the logarithm of the number of solutions of a random planted k-SAT formula concentrates around a deterministic n-independent threshold. Specically, if F k (;n ) is a random k-SAT formula on n variables, with clause density and with a uniformly drawn planted solution, there exists a function k( ) such that, besides for some in a set of Lesbegue measure zero, we have 1 logZ(F k (;n ))! k( ) in probability, where Z(F ) is the number of solutions of the formula F . This… 



On the concentration of the number of solutions of random satisfiability formulas

The assumption that the number of solutions concentrates, i.e., there exists a non‐random function α↦ϕs(α) such that, for any ε>0 , the assumption holds for all α<1, which proves the whole satisfiability regime of random 2‐SAT.

On the solution-space geometry of random constraint satisfaction problems

It is proved that much before solutions disappear, they organize into an exponential number of clusters, each of which is relatively small and far apart from all other clusters, which gives a satisfying intuitive explanation for the failure of the polynomial-time algorithms analyzed so far.

Algorithmic Barriers from Phase Transitions

It is proved that the set of k-colorings looks like a giant ball for k ges 2chi, but like an error-correcting code for k les (2 - epsiv)chi, and that an analogous phase transition occurs both in random k-SAT and in random hypergraph 2-coloring, which means that for each of these three problems, the location of the transition corresponds to the point where all known polynomial-time algorithms fail.

Mick gets some (the odds are on his side) (satisfiability)

  • V. ChvátalB. Reed
  • Mathematics
    Proceedings., 33rd Annual Symposium on Foundations of Computer Science
  • 1992
The authors present a linear-time algorithm that satisfies F with probability 1-o(1) whenever c<(0.25)2/sup k//k and establish a threshold for 2-SAT: if k = 2 then F is satisfiable with probability1-o (1) Whenever c<1 and unsatisfiable with probabilities 1-O(1), whenever c>1.

Reconstruction and Clustering in Random Constraint Satisfaction Problems

A set of technical conditions are formulated on a large family of random CSPs and bounds are proved on three most interesting thresholds for the density of such an ensemble: namely, the satisfiability threshold, the threshold for clustering of the solution space, and thereshold for an appropriate reconstruction problem on the CSPS.

Random 2-XORSAT at the Satisfiability Threshold

This study relies on the symbolic method and analytical tools coming from generating function theory which enable it to describe the evolution of n1/12 p(n, n/2(1 + µn-1/3)) as a function of µ.

The Satisfiability Threshold for k-XORSAT

  • B. PittelG. Sorkin
  • Mathematics, Computer Science
    Combinatorics, Probability and Computing
  • 2015
It is shown that m/n = 1 remains a sharp threshold for satisfiability of constrained k-XORSAT for every k ⩾ 3, and standard results on the 2-core of a random k-uniform hypergraph are used to extend this result to find the threshold for unconstrained k- XORSAT.

Sharp thresholds of graph properties, and the -sat problem

Consider G(n, p) to be the probability space of random graphs on n vertices with edge probability p. We will be considering subsets of this space defined by monotone graph properties. A monotone

The condensation transition in random hypergraph 2-coloring

This paper proves for the first time that a condensation transition exists in a natural random CSP, namely in random hypergraph 2-coloring, and finds that the second moment method applied to the number of 2-colorings breaks down strictly before the condensation Transition.

Gibbs states and the set of solutions of random constraint satisfaction problems

Empirical evidence suggests that local Monte Carlo Markov chain strategies are effective up to the clustering phase transition and belief propagation up toThe condensation point and refined message passing techniques (such as survey propagation) may also beat this threshold.