In this paper, we consider the reconfiguration problem of integer linear systems. In this problem, we are given an integer linear system I and two feasible solutions s and t of I, and then asked to transform s to t by changing a value of only one variable at a time, while maintaining a feasible solution of I throughout. $Z(I)$ for I is the complexity index introduced by Kimura and Makino (Discrete Applied Mathematics 200:67–78, 2016), which is defined by the sign pattern of the input matrix. We analyze the complexity of the reconfiguration problem of integer linear systems based on the complexity index $Z(I)$ of given I. We then show that the problem is (i) solvable in constant time if $Z(I)$ is less than one, (ii) weakly coNP-complete and pseudo-polynomially solvable if $Z(I)$ is exactly one, and (iii) PSPACE-complete if $Z(I)$ is greater than one. Since the complexity indices of Horn and two-variable-par-inequality integer linear systems are at most one, our results imply that the reconfiguration of these systems are in coNP and pseudo-polynomially solvable. Moreover, this is the first result that reveals coNP-completeness for a reconfiguration problem, to the best of our knowledge.

在本文中，我们考虑了整数线性系统的重配置问题。在这个问题中，我们给出了线性系统的整数余和两个可行解小号和吨的我，然后问转化小号到吨通过每次只改变一个变量的值，同时维持一个可行的解决方案我整个。$ž（\mathrm{一世}）$因为I是Kimura和Makino引入的复杂性指数（离散应用数学200：67–78，2016），由输入矩阵的符号模式定义。我们基于复杂度指标分析了整数线性系统重构问题的复杂度$ž（\mathrm{一世}）$给予我。然后，我们证明问题是（i）如果$ž（\mathrm{一世}）$ 小于1，（ii）如果满足以下条件，则弱coNP完全且伪多项式可解决 $ž（\mathrm{一世}）$ 恰好是一个，并且（iii）如果 $ž（\mathrm{一世}）$大于一。由于Horn和两个变量等式不等式整数线性系统的复杂度指数最多为1，因此我们的结果表明，这些系统的重新配置是coNP的，且伪多项式可求解。而且，据我们所知，这是第一个揭示重新配置问题的coNP完整性的结果。