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On the behaviour of random K-SAT on trees
KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.
Natl Inst Sci Educ & Res, Inst Phys Campus, Bhubaneswar, India .
2012 (English)In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, Vol. 2012, no 5, P05009- p.Article in journal (Refereed) Published
Abstract [en]

We consider the K-satisfiability problem on a regular d-ary rooted tree. For this model, we demonstrate how we can calculate in closed form the moments of the total number of solutions as a function of d and K, where the average is over all realizations for a fixed assignment of the surface variables. We find that different moments pick out different 'critical' values of d, below which they diverge as the total number of variables on the tree and above which they decay. We show that K-SAT on the random graph also behaves similarly. We also calculate exactly the fraction of instances that have solutions for all K. On the tree, this quantity decays to 0 (as the number of variables increases) for any d > 1. However, the recursion relations for this quantity have a non-trivial fixed point solution which indicates the existence of a different transition in the interior of an infinite rooted tree.

Place, publisher, year, edition, pages
2012. Vol. 2012, no 5, P05009- p.
Keyword [en]
exact results, networks, random graphs, solvable lattice models, typical-case computational complexity
National Category
Computer and Information Science
URN: urn:nbn:se:kth:diva-98527DOI: 10.1088/1742-5468/2012/05/P05009ISI: 000305266900011ScopusID: 2-s2.0-84861804100OAI: diva2:537912
Swedish Research CouncilICT - The Next Generation

QC 20120628

Available from: 2012-06-28 Created: 2012-06-27 Last updated: 2013-04-11Bibliographically approved

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Krishnamurthy, Supriya
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