用缠绕法逼近Holant问题
Approximating Holant problems by winding
摘要：
我们给出了一个FPRAS的Holant问题的奇偶性约束和不全相等的约束，计数无汇方向的问题的推广。该方法结合了一个采样器的近分配的“可缠绕”的功能-使用循环展开的典型路径技术的Jerrum和辛克莱-与一个约束的重量近分配。证明推广到一个更大的类的Holant问题，我们将这个类，并表明它不能扩展的表达减少。然后，我们问是否可绕性是等效的匹配电路（一个模拟的匹配门）的表达，并给出了肯定的答案为arity三的功能。
英文摘要：
We give an FPRAS for Holant problems with parity constraints and not-all-equal constraints, a generalisation of the problem of counting sink-free-orientations. The approach combines a sampler for near-assignments of "windable" functions -- using the cycle-unwinding canonical paths technique of Jerrum and Sinclair -- with a bound on the weight of near-assignments. The proof generalises to a larger class of Holant problems; we characterise this class and show that it cannot be extended by expressibility reductions. We then ask whether windability is equivalent to expressibility by matchings circuits (an analogue of matchgates), and give a positive answer for functions of arity three.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
