Flashback: A Reversible Bilateral Run-Peeling Decomposition of Strings

TL;DR

Flashback introduces a reversible string decomposition method that efficiently peels maximal character runs from strings, with a proven run-pairing theorem and structural properties, applicable in linear time and space.

Contribution

The paper presents a novel reversible bilateral run-peeling decomposition with a run-pairing theorem and structural insights, matching lower bounds for string tokenization.

Findings

Decomposition and reconstruction run in O(n) time and space.

Flashback's token count is optimal, matching a lower bound.

Structural properties include characterisation of palindromes and finite-state representation.

Abstract

We introduce Flashback, a reversible string decomposition that repeatedly peels the maximal leading and trailing character runs from a sentinel-wrapped input, recording each pair as one bilateral token. Decomposition and reconstruction both run in O(n) time and space. Our central result is a run-pairing theorem: Flashback is equivalent to pairing the first run of the string with the last, the second with the second-to-last, and so on. This gives an exact token count of 1+[r/2] for a string with r maximal runs, and matches a lower bound that holds for any admissible bilateral run-peeling scheme. From the run-pairing theorem the main structural properties follow as corollaries: the irreducible peeling kernel uses at most two symbols; palindromes are precisely the strings whose run-length encoding is symmetric with an odd number of runs; the image of the decomposition admits an explicit finite-state characterisation; and changing one run length rewrites exactly one content token.