Dynamic direct (ranked) access of MSO query evaluation over SLP-compressed strings

TL;DR

This paper introduces an efficient algorithm for MSO query evaluation over strings and their SLP compression, supporting dynamic edits with fast access, improving previous methods in speed and applicability.

Contribution

It extends direct MSO query access algorithms to SLP-compressed strings with dynamic editing capabilities, achieving logarithmic query time after linear preprocessing.

Findings

Linear-time preprocessing for MSO query answers

Logarithmic time retrieval of answers over SLP-compressed strings

Efficient handling of dynamic edits on SLPs

Abstract

We present an algorithm that, given an index $t$, produces the $t$-th (lexicographically ordered) answer of an MSO query over a string. The algorithm requires linear-time preprocessing, and builds a data structure that answers each of these calls in logarithmic time. We then show how to extend this algorithm for a string that is compressed by a straight-line program (SLP), also with linear-time preprocessing in the (compressed encoding of the) string, and maintaining direct access in logtime of the original string. Lastly, we extend the algorithm by allowing complex edits on the SLP after the direct-access data structure has been processsed, which are translated into the data structure in logtime. We do this by adapting a document editing framework introduced by Schmid and Schweikardt (PODS 2022). This work improves on a recent result of dynamic direct access of MSO queries over strings (Bourhis et. al., ICDT 2025) by a log-factor on the access procedure, and by extending the results to SLPs.