An Analysis of Decision Problems for Relational Pattern Languages under Various Constraints
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914619967143936 |
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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 |
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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 |