Longest segment of balanced parentheses -- an exercise in program inversion in a segment problem (Functional Pearl)

TL;DR

This paper presents a linear-time solution for finding the longest balanced parentheses segment, combining segment problem techniques with function inversion and shift-reduce parsing methods.

Contribution

It introduces a novel approach that integrates segment problem strategies with function inversion and shift-reduce parsing for balanced parentheses.

Findings

Linear-time algorithm for longest balanced segment

Innovative use of function inversion in segment problems

Application of shift-reduce parsing techniques

Abstract

Given a string of parentheses, the task is to find the longest consecutive segment that is balanced, in linear time. We find this problem interesting because it involves a combination of techniques: the usual approach for solving segment problems, and a theorem for constructing the inverse of a function -- through which we derive an instance of shift-reduce parsing.