区间矩阵的AE正则性
AE regularity of interval matrices
AI总结：
本文研究了区间矩阵的AE正则性，探讨了系数矩阵的性质以保证AE解的存在性，并提出了AE正则性的定义，讨论了其刻画方法以及各种隐含AE正则的矩阵类，同时指出了与计算复杂度相关的开放问题。
摘要：
考虑具有区间系数的线性方程组，每个区间系数关联于全称或存在量词。通过$ orall\exists$-量词定义系统的AE解集和AE可解性。本文探讨了系数矩阵应具备何种性质以保证AE解的存在性。基于此动机，我们引入了AE正则性的概念，其意味着AE解集非空且对于任意右端向量系统都是AE可解的。我们讨论了AE正则性的刻画，并聚焦于各种隐含AE正则的矩阵类。其中一些类是多项式可判定的，因此提供了高效检查AE正则性的方法。我们还陈述了与计算复杂度和刻画相关的开放问题。
英文摘要：
Consider a linear system of equations with interval coefficients, and each interval coefficient is associated with either a universal or an existential quantifier. The AE solution set and AE solvability of the system is defined by $\forall\exists$-quantification. Herein, we deal with the problem what properties must the coefficient matrix have in order that there is guaranteed an existence of an AE solution. Based on this motivation, we introduce a concept of AE regularity, which implies that the AE solution set is nonempty and the system is AE solvable for every right-hand side. We discuss characterization of AE regularity, and we also focus on various classes of matrices that are implicitly AE regular. Some of these classes are polynomially decidable, and therefore give an efficient way for checking AE regularity. We also state open problems related to computational complexity and characterization.
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。
