Exact location of the phase transition for random (1,2)-QSAT
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 49 (2015) no. 1, pp. 23-45.

The QSAT problem is the quantified version of the SAT problem. We show the existence of a threshold effect for the phase transition associated with the satisfiability of random quantified boolean CNF formulas of the form XYϕ(X,Y), where X has m variables, Y has n variables and each clause in ϕ has one literal from X and two from Y. For such formulas, we show that the threshold phenomenon is controlled by the ratio between the number of clauses and the number n of existential variables. Then we give the exact location of the associated critical ratio c * : it is a decreasing function of α, where α is the limiting value of m/log(n) when n tends to infinity. Thus we give a precise location of the phase transition associated with a coNP-complete problem.

Reçu le :
Accepté le :
DOI : 10.1051/ita/2014025
Classification : 68R01, 60C05, 05A16
Mots-clés : Random quantified formulas, satisfiability, phase transition, sharp threshold
Creignou, Nadia 1 ; Daudé, Hervé 2 ; Egly, Uwe 3 ; Rossignol, Raphaël 4, 5

1 Aix-Marseille Université, CNRS, LIF UMR 7279, 13288 Marseille, France
2 Aix-Marseille Université, CNRS, I2M UMR 7373, 13453 Marseille, France
3 Institut für Informationsysteme 184/3, Technische Universität Wien, Favoritenstrasse 9-11 A-1040 Wien, Austria
4 University Grenoble Alpes, IF, 38000 Grenoble, France
5 CNRS, IF, 38000 Grenoble, France
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     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
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Creignou, Nadia; Daudé, Hervé; Egly, Uwe; Rossignol, Raphaël. Exact location of the phase transition for random (1,2)-QSAT. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 49 (2015) no. 1, pp. 23-45. doi : 10.1051/ita/2014025. http://archive.numdam.org/articles/10.1051/ita/2014025/

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