Ranked MSO-enumeration over compressed words

2026-06-02

AI Summary

This work addresses the problem of efficiently enumerating the results of a fixed monadic second-order (MSO) query over strings represented in straight-line program (SLP) compressed form, while outputting them in an MSO-definable order. The authors extend the factorization tree technique to the setting of compressed strings for the first time, integrating SLP representations, MSO logic, and constant-delay enumeration methods. Their approach achieves linear preprocessing time and constant delay between consecutive outputs in the desired order. As a consequence, it enables efficient left-to-right enumeration of symbols resulting from any fixed multi-regular function applied to the compressed string. This significantly enhances the practicality and efficiency of structured querying over highly compressed data.

Abstract

It is shown that the ranked query enumeration problem for a fixed MSO-query on strings can be solved with linear preprocessing and constant delay in the grammar-compressed setting, where the input string is given by a so-called straight-line program, i.e., a context-free grammar that produces exactly one string. Moreover, `ranked' means that the output tuples of the MSO-query are printed in a specific order that has to be MSO-definable. This is the first result for ranked query enumeration on compressed data. A corollary of this result is that for a fixed polyregular function $f$ and a word $w$ that is given by a straight-line program of size $n$, one can list after preprocessing time $\mathcal{O}(n)$ the symbols in $f(w)$ from left to right with constant delay, which generalizes a result of Bojanczyk for the case where $w$ is uncompressed. The proofs for these results are based on factorization trees, which are made accessible to the grammar-compressed setting (a contribution of independent interest).

Problem

• ranked enumeration
• MSO query
• compressed words
• straight-line program
• grammar-compressed

Innovation

• ranked enumeration
• MSO queries
• grammar-compressed strings
• straight-line programs
• factorization trees