Parameterized String Equations

TL;DR

This paper analyzes the computational complexity of systems of string equations, providing polynomial algorithms for simple cases and proving hardness results for more complex instances, with implications for string manipulation problems.

Contribution

It introduces a complexity framework for string equations, offering polynomial-time solutions for size-2 systems and hardness results for larger systems, along with algorithms for deletion variants.

Findings

Polynomial-time algorithm for size-2 equations

Hardness results for size-3 and two-equation systems

XP algorithms for deletion-allowed variants with few variables

Abstract

We study systems of String Equations where block variables need to be assigned strings so that their concatenation gives a specified target string. We investigate this problem under a multivariate complexity framework, searching for tractable special cases such as systems of equations with few block variables or few equations. Our main results include a polynomial-time algorithm for size-2 equations, and hardness for size-3 equations, as well as hardness for systems of two equations, even with tight constraints on the block variables. We also study a variant where few deletions are allowed in the target string, and give XP algorithms in this setting when the number of block variables is constant.