| 有限域上线性方程组的相变现象 |
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| 引用本文： | 沈静,李薇,艾小川.有限域上线性方程组的相变现象[J].舰船电子工程,2011,31(1):54-57,79. |
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| 作者姓名： | 沈静 李薇 艾小川 |
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| 作者单位： | 海军工程大学理学院应用数学系,武汉,430033 |
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| 摘 要： | 对于含有n个未知数t个方程的线性方程组，各种实验显示随着参数r（方程个数／未知数个数）的变化，会发生从有解到无解的相变现象。研究工随机产生的有限域F上的k-线性方程组（每个线性方程中只含有k个变量）的相变现象，给出了k-线性方程组相变点的上界和下界。
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| 关 键 词： | 线性方程组 可满足性 相变现象 |
On the Phase Transitions of Linear Systems Over Finite Fields |
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| Shen Jing,Li Wei,Ai Xiaochuan.On the Phase Transitions of Linear Systems Over Finite Fields[J].Ship Electronic Engineering,2011,31(1):54-57,79. |
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| Authors: | Shen Jing Li Wei Ai Xiaochuan |
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| Institution: | Shen Jing Li Wei Ai Xiaochuan(Department of Mathematics,School of Science,Naval University of Engineering,Wuhan 430033) |
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| Abstract: | Various experimental investigations have shown phase transitions between satisfiability and unsatisfiability of linear systems with t equations over n variables as r(the ratio of the number of equations to the number of variables) is varied.We study the phase transitions of random k-linear systems with k variables per equation,give the lower bound and the upper bound of the threshold point. |
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| Keywords: | linear systems satisfiability phase transition |
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