Complexity of testing morphic primitivity
Vojt\v{e}ch Matocha, \v{S}t\v{e}p\'an Holub
TL;DR
This paper improves the understanding of the computational complexity of testing whether a word is a fixed point of a nontrivial morphism, providing an efficient O(mn) algorithm.
Contribution
It presents an optimized implementation of Holub's algorithm with a proven complexity of O(mn), enhancing the efficiency of testing morphic primitivity.
Findings
Algorithm runs in O(mn) time
Efficient implementation for fixed point testing
Improved complexity bounds for morphic primitivity
Abstract
We analyze the algorithm in [Holub, 2009], which decides whether a given word is a fixed point of a nontrivial morphism. We show that it can be implemented to have complexity in O(mn), where n is the length of the word and m the size of the alphabet.
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Taxonomy
Topicssemigroups and automata theory · Machine Learning and Algorithms · Algorithms and Data Compression