We consider the computational complexity of reconfiguration problems, in which one is given two combinatorial configurations satisfying some constraints, and is asked to transform one into the other using elementary operations, while satisfying the constraints at all times. Such problems appear naturally in many contexts, such as model checking, motion planning, enumeration, sampling, and recreational mathematics. We provide hardness results for problems in this family, in which the constraints and operations are particularly simple.

More precisely, we prove the PSPACE-completeness of the following decision problems:

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Given two satisfying assignments of a planar monotone instance of NAE 3-SAT, can one assignment be transformed into the other by a sequence of variable flips such that the formula remains satisfied at every step?

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Given two subsets of a set S of integers with the same sum, can one subset be transformed into the other by adding or removing at most three elements of S at a time, such that the intermediate subsets also have the same sum?

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Given two points in ${\{0,1\}}^n$ contained in a polytope P specified by a constant number of linear inequalities, is there a path in the n-hypercube connecting the two points and contained in P?

我们考虑了重新配置问题的计算复杂性，其中给了一个满足某些约束的两个组合配置，并要求他们使用基本运算将一个转换为另一个，同时始终满足约束。这样的问题在许多情况下自然出现，例如模型检查，运动计划，枚举，采样和娱乐数学。我们为该系列中的问题提供硬度结果，其中的约束和操作特别简单。

更准确地说，我们证明了以下决策问题的PSPACE-完整性：

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给定NAE 3-SAT的平面单调实例的两个令人满意的分配，是否可以通过一系列可变翻转将一个分配转换为另一个分配，以使公式在每一步都保持满足？

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给定一组整数S的两个子集具有相同的总和，是否可以通过一次最多添加或删除S的三个元素来将一个子集转换为另一个子集，以使中间子集也具有相同的总和？

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给定两点 ${\{0，\mathrm{1个}\}}^{ñ}$包含在由恒定数目的线性不等式指定的多面体P中的n超超立方体中是否存在一条连接这两点并包含在P中的路径？