Result: Phase transitions of PP-complete satisfiability problems

Title:
Phase transitions of PP-complete satisfiability problems
Authors:
BAILEY, Delbert D, DALMAU, Victor, KOLAITIS, Phokion G
Source:
SAT 2001, the fourth international symposium on the theory and applications of satisfiability testingDiscrete applied mathematics. 155(12):1627-1639
Publisher Information:
Amsterdam; Lausanne; New York, NY: Elsevier, 2007.
Publication Year:
2007
Physical Description:
print, 28 ref
Original Material:
INIST-CNRS
Subject Terms:
Control theory, operational research, Automatique, recherche opérationnelle, Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Combinatoire. Structures ordonnées, Combinatorics. Ordered structures, Combinatoire, Combinatorics, Sciences appliquees, Applied sciences, Informatique; automatique theorique; systemes, Computer science; control theory; systems, Informatique théorique, Theoretical computing, Automates. Machines abstraites. Machines de turing, Automata. Abstract machines. Turing machines, Algorithmique. Calculabilité. Arithmétique ordinateur, Algorithmics. Computability. Computer arithmetics, Assignation, Assignment, Asignación, Borne inférieure, Lower bound, Cota inferior, Borne supérieure, Upper bound, Cota superior, Classe complexité, Complexity class, Clase complejidad, Combinatoire, Combinatorics, Combinatoria, Ensemble aléatoire, Random set, Conjunto aleatorio, Informatique théorique, Computer theory, Informática teórica, Loi probabilité, Probability distribution, Ley probabilidad, Machine Turing, Turing machine, Máquina Turing, Modification, Modificación, Moyenne, Average, Promedio, Méthode moindre carré, Least squares method, Método cuadrado menor, Optimisation, Optimization, Optimización, Probabilité, Probability, Probabilidad, Problème NP complet, NP complete problem, Problema NP completo, Problème satisfiabilité, Satisfiability problem, Problema satisfactibilidad, Procédure, Procedure, Procedimiento, Racine carrée, Square root, Raíz cuadrada, Résultat expérimental, Experimental result, Resultado experimental, Temps polynomial, Polynomial time, Tiempo polinomial, Transition phase, Phase transitions, Transición fase, 68Q05, Problème décision, Satisfiabilité, Vérité, PP-complete, Satisfiability
Document Type:
Conference Conference Paper
File Description:
text
Language:
English
Author Affiliations:
compttter Science Department, University of California, Santa Cruz, Sauta Cruz, CA 95064, United States
Departament de tecnologia, Universitat Pompeu Fabra,Estació de Fronça, Passeig de la circumval.lació 8, Barcelona 08003, Spain
ISSN:
0166-218X
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=18962803
Rights:
Copyright 2008 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Computer science; theoretical automation; systems

Mathematics
Accession Number:
edscal.18962803
Database:
PASCAL Archive

Further Information

The complexity class PP consists of all decision problems solvable by polynomial-time probabilistic Turing machines. It is well known that PP is a highly intractable complexity class and that PP-complete problems are in all likelihood harder than NP-complete problems. We investigate the existence of phase transitions for a family of PP-complete Boolean satisfiability problems under the fixed clauses-to-variables ratio model. A typical member of this family is the decision problem # 3SAT( ≥ 2n/2): given a 3CNF-formula, is it satisfied by at least the square-root of the total number of possible truth assignments? We provide evidence to the effect that there is a critical ratio r3,2at which the asymptotic probability of # 3SAT( ≥2n/2) undergoes a phase transition from to 0. We obtain upper and lower bounds for r3,2 by showing that 0.9227 ≤ r3,2 ≤ 2.595. We also carry out a set of experiments on random instances of # 3SAT( ≥ 2n/2) using a natural modification of the Davis-Putnam-Logemann-Loveland (DPLL) procedure. Our experimental results suggest that r3,2 ≈ 2.5. Moreover, the average number of recursive calls of this modified DPLL procedure reaches a peak around 2.5 as well.