Counting Subwords in Circular Words and Their Parikh Matrices
Abstract
The word inference problem is to determine languages such that the information on the number of occurrences of those subwords in the language can uniquely identify a word. A considerable amount of work has been done on this problem, but the same cannot be said for circular words despite growing interests on the latter due to their applications -- for example, in splicing systems. Meanwhile, Parikh matrices are useful tools and well established in the study of subword occurrences. In this work, we propose two ways of counting subword occurrences in circular words. We then extend the idea of Parikh matrices to the context of circular words and investigate this extension. Motivated by the word inference problem, we study ambiguity in the identification of a circular word by its Parikh matrix. Accordingly, two rewriting rules are developed to generate ternary circular words which share the same Parikh matrix.
Keywords
Cite
@article{arxiv.2110.14858,
title = {Counting Subwords in Circular Words and Their Parikh Matrices},
author = {Ghajendran Poovanandran and Jamie Simpson and Wen Chean Teh},
journal= {arXiv preprint arXiv:2110.14858},
year = {2021}
}
Comments
Preprint, Submitted for journal consideration