Random 2-SAT Solution Components and a Fitness Landscape - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2011

Random 2-SAT Solution Components and a Fitness Landscape

Abstract

We describe a limiting distribution for the number of connected components in the subgraph of the discrete cube induced by the satisfying assignments to a random 2-SAT formula. We show that, for the probability range where formulas are likely to be satisfied, the random number of components converges weakly (in the number of variables) to a distribution determined by a Poisson random variable. The number of satisfying assignments or solutions is known to grow exponentially in the number of variables. Thus, our result implies that exponentially many solutions are organized into a stochastically bounded number of components. We also describe an application to biological evolution; in particular, to a type of fitness landscape where satisfying assignments represent viable genotypes and connectivity of genotypes is limited by single site mutations. The biological result is that, with probability approaching 1, each viable genotype is connected by single site mutations to an exponential number of other viable genotypes while the number of viable clusters is finite.
Fichier principal
Vignette du fichier
1024-6321-1-PB.pdf (347.65 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00990478 , version 1 (13-05-2014)

Identifiers

Cite

Damien Pitman. Random 2-SAT Solution Components and a Fitness Landscape. Discrete Mathematics and Theoretical Computer Science, 2011, Vol. 13 no. 2 (2), pp.45--62. ⟨10.46298/dmtcs.534⟩. ⟨hal-00990478⟩

Collections

TDS-MACS
71 View
1025 Download

Altmetric

Share

Gmail Facebook X LinkedIn More