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dc.contributor.authorPitman, Damien J.
dc.date.accessioned2016-09-19T20:41:15Z
dc.date.available2016-09-19T20:41:15Z
dc.date.issued2011
dc.identifier.citationDamien Pitman. Random 2-SAT Solution Components and a Fitness Landscape. Discrete Mathematics & Theoretical Computer Science, 2011, 13 (2), pp.45–62.en_US
dc.identifier.issn1365-8050
dc.identifier.urihttps://scholarworks.montana.edu/xmlui/handle/1/10018
dc.description.abstractWe 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.en_US
dc.titleRandom 2-SAT Solution Components and a Fitness Landscapeen_US
dc.typeArticleen_US
mus.citation.extentfirstpage45en_US
mus.citation.extentlastpage62en_US
mus.citation.issue2en_US
mus.citation.journaltitleDiscrete Mathematics & Theoretical Computer Scienceen_US
mus.citation.volume13en_US
mus.identifier.categoryPhysics & Mathematicsen_US
mus.relation.collegeCollege of Letters & Scienceen_US
mus.relation.departmentMathematical Sciences.en_US
mus.relation.universityMontana State University - Bozemanen_US


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