Detecting patterns in finite regular and context-free languages

2009/06/17 by Narad Rampersad, Jeffrey Shallit, Rampersad, Narad +1
Computer Science · #Algorithms and Data Compression #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #Machine Learning and Algorithms #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0906.3220

openalex publication_date 2009/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider variations on the following problem: given an NFA M and a pattern p, does there exist an x in L(M) such that p matches x? We consider the restricted problem where M only accepts a finite language. We also consider the variation where the pattern p is required only to match a factor of x. We show that both of these problems are NP-complete. We also consider the same problems for context-free grammars; in this case the problems become PSPACE-complete.

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