关于字符串约束的可分性问题
On the Separability Problem of String Constraints
摘要：
我们解决直线字符串约束的可分性问题。类C的语言被类S分离的问题是：给定C中的两种语言A和B，S中是否存在分离A和B的语言I（即，I是A的超集，与B不相交）。字符串约束的可分性与字符串约束插值的基本问题相同。我们首先证明了直线串约束的正则可分性是不可判定的。我们的第二个结果是分段可测试语言的直线字符串约束的可分性问题的可判定性，虽然精确的复杂性是开放的。在我们的第三个结果中，我们考虑分段可测试语言的正片段作为分离器，并获得了一类有用的直线串约束的可分离性的EXPSPACE算法，以及PSPACE-硬度结果。
英文摘要：
We address the separability problem for straight-line string constraints. The separability problem for languages of a class C by a class S asks: given two languages A and B in C, does there exist a language I in S separating A and B (i.e., I is a superset of A and disjoint from B)? The separability of string constraints is the same as the fundamental problem of interpolation for string constraints. We first show that regular separability of straight line string constraints is undecidable. Our second result is the decidability of the separability problem for straight-line string constraints by piece-wise testable languages, though the precise complexity is open. In our third result, we consider the positive fragment of piece-wise testable languages as a separator, and obtain an EXPSPACE algorithm for the separability of a useful class of straight-line string constraints, and a PSPACE-hardness result.
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