耦合XORSAT公式的解空间
The Space of Solutions of Coupled XORSAT Formulae
摘要：
XOR可满足性（XORSAT）问题处理$n$布尔变量和$m$子句的系统。每个子句都是变量子集的线性布尔方程（XOR）。$K$ -子句是涉及$K$不同变量的子句。在随机$K$ -XORSAT问题中，通过从$n$变量的所有可能子句的集合中随机一致地选择$m$ $K$ -子句来创建公式.当比值$\frac{m}{n}$变化时，随机公式的解的集合表现出各种几何转变。我们考虑一个{ \em耦合} $K$ -XORSAT系综，由一个链的随机XORSAT模型，空间耦合在一个有限的窗口沿链方向。我们观察到，阈值饱和现象发生在这个合奏，我们描述了各种性质的空间的解决方案，这样的耦合公式。
英文摘要：
The XOR-satisfiability (XORSAT) problem deals with a system of $n$ Boolean variables and $m$ clauses. Each clause is a linear Boolean equation (XOR) of a subset of the variables. A $K$-clause is a clause involving $K$ distinct variables. In the random $K$-XORSAT problem a formula is created by choosing $m$ $K$-clauses uniformly at random from the set of all possible clauses on $n$ variables. The set of solutions of a random formula exhibits various geometrical transitions as the ratio $\frac{m}{n}$ varies. We consider a {\em coupled} $K$-XORSAT ensemble, consisting of a chain of random XORSAT models that are spatially coupled across a finite window along the chain direction. We observe that the threshold saturation phenomenon takes place for this ensemble and we characterize various properties of the space of solutions of such coupled formulae.
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