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Computer Science > Formal Languages and Automata Theory

arXiv:2411.07275 (cs)
[Submitted on 11 Nov 2024]

Title:The Equivalence Problem of E-Pattern Languages with Regular Constraints is Undecidable

Authors:Dirk Nowotka, Max Wiedenhöft
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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. Regular constraints restrict valid substitutions of variables by associating with each variable a regular language representable by, e.g., finite automata. Pattern languages with regular constraints contain only words in which each variable is substituted according to a set of regular constraints. We consider the membership, inclusion, and equivalence problems for erasing and non-erasing pattern languages with regular constraints. Our main result shows that the erasing equivalence problem, one of the most prominent open problems in the realm of patterns, becomes undecidable if regular constraints are allowed in addition to variable equality.
Comments: 13 pages with references, 1 table, accepted and published at CIAA 2024. arXiv admin note: substantial text overlap with arXiv:2411.06904
Subjects: Formal Languages and Automata Theory (cs.FL); Computational Complexity (cs.CC); Combinatorics (math.CO)
MSC classes: 68R15
ACM classes: F.4.3
Cite as: arXiv:2411.07275 [cs.FL]
  (or arXiv:2411.07275v1 [cs.FL] for this version)
  https://doi.org/10.48550/arXiv.2411.07275

Submission history

From: Max Wiedenhöft [view email]
[v1] Mon, 11 Nov 2024 13:12:06 UTC (34 KB)
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