Knowledge Management System of Institute of Theoretical Physics, CAS
Zhou, Haijun; Zhou, HJ , Chinese Acad Sci, Inst Theoret Phys, Beijing 100080, Peoples R China | |
T -> 0 mean-field population dynamics approach for the random 3-satisfiability problem | |
Source Publication | PHYSICAL REVIEW E |
Keyword | K-satisfiability Problem Computational-complexity Cavity Method Phase Entropy States |
Abstract | During the past decade, phase-transition phenomena in the random 3-satisfiability (3-SAT) problem has been intensively studied by statistical physics methods. In this work, we study the random 3-SAT problem by the mean-field first-step replica-symmetry-broken cavity theory at the limit of temperature T -> 0. The reweighting parameter y of the cavity theory is allowed to approach infinity together with the inverse temperature beta with fixed ratio r=y/beta. Focusing on the system's space of satisfiable configurations, we carry out extensive population dynamics simulations using the technique of importance sampling, and we obtain the entropy density s(r) and complexity Sigma(r) of zero-energy clusters at different r values. We demonstrate that the population dynamics may reach different fixed points with different types of initial conditions. By knowing the trends of s(r) and Sigma(r) with r, we can judge whether a certain type of initial condition is appropriate at a given r value. This work complements and confirms the results of several other very recent theoretical studies. |
2008 | |
ISSN | 1539-3755 |
Volume | 77Issue:6Pages:- |
Subject Area | Physics |
Indexed By | SCI |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.itp.ac.cn/handle/311006/5524 |
Collection | 理论物理所科研产出_SCI论文 |
Corresponding Author | Zhou, HJ , Chinese Acad Sci, Inst Theoret Phys, Beijing 100080, Peoples R China |
Recommended Citation GB/T 7714 | Zhou, Haijun,Zhou, HJ , Chinese Acad Sci, Inst Theoret Phys, Beijing 100080, Peoples R China. T -> 0 mean-field population dynamics approach for the random 3-satisfiability problem[J]. PHYSICAL REVIEW E,2008,77(6):-. |
APA | Zhou, Haijun,&Zhou, HJ , Chinese Acad Sci, Inst Theoret Phys, Beijing 100080, Peoples R China.(2008).T -> 0 mean-field population dynamics approach for the random 3-satisfiability problem.PHYSICAL REVIEW E,77(6),-. |
MLA | Zhou, Haijun,et al."T -> 0 mean-field population dynamics approach for the random 3-satisfiability problem".PHYSICAL REVIEW E 77.6(2008):-. |
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