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An Analysis of Decision Problems for Relational Pattern L...
[Submitted on 8 Dec 2025 (v1), last revised 21 Jul 2026 (this ve · 2025-12-08 · via math updates on arXiv.org

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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, 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.

Submission history

From: Max Wiedenhöft [view email]
[v1] Mon, 8 Dec 2025 11:59:02 UTC (66 KB)
[v2] Fri, 27 Mar 2026 22:31:59 UTC (68 KB)
[v3] Sat, 30 May 2026 09:58:59 UTC (61 KB)
[v4] Tue, 21 Jul 2026 12:39:27 UTC (67 KB)