On the Separability Problem of String Constraints

by   Parosh Aziz Abdulla, et al.

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.



There are no comments yet.


page 1

page 2

page 3

page 4


What Is Decidable about String Constraints with the ReplaceAll Function

Recently, it was shown that any theory of strings containing the string-...

On formally undecidable propositions in nondeterministic languages

Any class of languages 𝐋 accepted in time 𝐓 has a counterpart 𝐍𝐋 accepte...

Solving String Constraints With Regex-Dependent Functions Through Transducers With Priorities And Variables

Regular expressions are a classical concept in formal language theory. R...

On Problems Dual to Unification: The String-Rewriting Case

In this paper, we investigate problems which are dual to the unification...

A critical analysis of string APIs: The case of Pharo

Most programming languages, besides C, provide a native abstraction for ...

A New Implementation of Manacher's Algorithm

Manacher's algorithm is optimal for the longest palindromic substring pr...

Parameterized String Equations

We study systems of String Equations where block variables need to be as...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.