Separating Many Words by Counting Occurrences of Factors

Saarela, Aleksi

doi:10.1007/978-3-030-24886-4_19

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2021

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“…multiset of all non-contiguous subwords of length at most k) was investigated. Some other works on k-spectra include [7,9,21].…”

Section: Introductionmentioning

confidence: 99%

Counting Subwords in Circular Words and Their Parikh Matrices

Poovanandran¹,

Simpson²,

Teh³

2021

Preprint

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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.

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“…multiset of all non-contiguous subwords of length at most k) was investigated. Some other works on k-spectra include [7,9,21].…”

Section: Introductionmentioning

confidence: 99%