计算机科学 ›› 2016, Vol. 43 ›› Issue (4): 33-36.doi: 10.11896/j.issn.1002-137X.2016.04.006

• 2015年全国理论计算机科学学术年会 • 上一篇    下一篇

正则3-SAT问题的相变现象

张明明,许道云   

  1. 贵州大学计算机科学与技术学院 贵阳550025,贵州大学计算机科学与技术学院 贵阳550025
  • 出版日期:2018-12-01 发布日期:2018-12-01
  • 基金资助:
    本文受国家自然科学基金(61262006)资助

Phase Transition Phenomenon of Regular 3-SAT Problem

ZHANG Ming-ming and XU Dao-yun   

  • Online:2018-12-01 Published:2018-12-01

摘要: 通过对3-CNF公式加以限制,要求其中每个变元出现的次数相同,引出正则3-SAT问题。进一步,通过对两种子句产生机制形成的(3,s)-CNF公式进行可满足性观察,发现在规模较小的情况下,正则3-CNF公式比非正则3-CNF公式更容易满足。从而推测与非正则3-SAT问题相比,正则3-SAT问题的相变点有偏移现象。最后,从变元自由度的角度对这一现象给出了定性解释。

关键词: 正则CNF公式,SAT问题,相变,变元自由度

Abstract: We considered the restriction on the 3-CNF formula on n Boolean variables{x1,x2,…,xn},in which each of the 2n literals occurs precisely {x1,x1,…,xn,xn} times.We called such formulas as regular (3,s)-CNF formulas.Through the two kinds of clauses generating mechanism of (3,s)-CNF formula,we observed that the regular (3,s)-CNF formulas are easier to be satisfied than non-regular 3-CNF formulas while the input size is small.Thus we inferred that compared with non-regular 3-SAT,the transition point of regular 3-SAT problems has offset phenomenon.Finally we explained this phenomenon from a perspective of the number of the variable’s degree of freedom.

Key words: Regular CNF formula,SAT problem,Phase transition,Variable’s degrees of freedom

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