Detecting palindromes, patterns, and borders in regular languages

TL;DR

This paper investigates the computational complexity of problems related to automata and various special language classes, such as palindromes and bordered words, focusing on membership, infiniteness, and shortest word length.

Contribution

It provides new insights into the decidability and complexity of automata problems for complex language classes, including palindromes, borders, and pattern matching.

Findings

Decidability results for automata accepting words in specific language classes

Complexity bounds for shortest word length in these classes

Algorithms for membership and infiniteness problems

Abstract

Given a language L and a nondeterministic finite automaton M, we consider whether we can determine efficiently (in the size of M) if M accepts at least one word in L, or infinitely many words. Given that M accepts at least one word in L, we consider how long a shortest word can be. The languages L that we examine include the palindromes, the non-palindromes, the k-powers, the non-k-powers, the powers, the non-powers (also called primitive words), the words matching a general pattern, the bordered words, and the unbordered words.