An Analysis of Decision Problems for Relational Pattern Languages under Various Constraints

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Main Authors: Jansen, Klaus, Nowotka, Dirk, Pirotton, Lis, Wambsganz, Corinna, Wiedenhöft, Max
Format: Preprint
Published: 2025
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author Jansen, Klaus
Nowotka, Dirk
Pirotton, Lis
Wambsganz, Corinna
Wiedenhöft, Max
author_facet Jansen, Klaus
Nowotka, Dirk
Pirotton, Lis
Wambsganz, Corinna
Wiedenhöft, Max
contents 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, achieved by using regular patterns and relating individual variables independently from the patterns structure separately. 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.
format Preprint
id arxiv_https___arxiv_org_abs_2512_07476
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle An Analysis of Decision Problems for Relational Pattern Languages under Various Constraints
Jansen, Klaus
Nowotka, Dirk
Pirotton, Lis
Wambsganz, Corinna
Wiedenhöft, Max
Formal Languages and Automata Theory
Computational Complexity
Combinatorics
68R15
F.4.3
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, achieved by using regular patterns and relating individual variables independently from the patterns structure separately. 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.
title An Analysis of Decision Problems for Relational Pattern Languages under Various Constraints
topic Formal Languages and Automata Theory
Computational Complexity
Combinatorics
68R15
F.4.3
url https://arxiv.org/abs/2512.07476