An Analysis of Decision Problems for Relational Pattern Languages under Various Constraints
Abstract
Patterns are words with terminals and variables. The language of a pattern is the set of words obtained by uniformly substituting all variables with words that contain only terminals. In their original definition, patterns only allow for multiple distinct occurrences of some variables to be related by the equality relation, represented by using the same variable multiple times. In an extended notion, called relational patterns and relational pattern languages, variables may be related by arbitrary other relations. We extend the ongoing investigation of the main decision problems for patterns (namely, the equivalence problem, the inclusion problem, and the membership problem) to relational pattern languages under a wide range of relevant individual relations, providing a comprehensive foundation in all three research directions.
Cite
@article{arxiv.2512.07476,
title = {An Analysis of Decision Problems for Relational Pattern Languages under Various Constraints},
author = {Klaus Jansen and Dirk Nowotka and Lis Pirotton and Corinna Wambsganz and Max Wiedenhöft},
journal= {arXiv preprint arXiv:2512.07476},
year = {2026}
}
Comments
44 pages (incl. appendix and references); 4 tables; restructured and updated; extended version of the paper submitted to CIAA 2026