PROPERTIES AND CONSTRUCTION OF UNIQUE MAXIMAL FACTORIZATION FAMILIES FOR STRINGS

We say a family $\mathcal{W}$ of strings over an alphabet is an UMFF if every string has a unique maximal factorization over $\mathcal{W}$ . Foundational work by Chen, Fox and Lyndon established properties of the Lyndon circ-UMFF, which is based on lexicographic ordering. Commencing with the circ-UM...

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Bibliographic Details
Published in:International journal of foundations of computer science 2008-08, Vol.19 (4), p.1073-1084
Main Authors: DAYKIN, DAVID E., DAYKIN, JACQUELINE W.
Format: Article
Language:English
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Summary:We say a family $\mathcal{W}$ of strings over an alphabet is an UMFF if every string has a unique maximal factorization over $\mathcal{W}$ . Foundational work by Chen, Fox and Lyndon established properties of the Lyndon circ-UMFF, which is based on lexicographic ordering. Commencing with the circ-UMFF related to V-order, we then proved analogous factorization families for a further 32 Block-like binary orders. Here we distinguish between UMFFs and circ-UMFFs, and then study the structural properties of circ-UMFFs. These properties give rise to the complete construction of any circ-UMFF. We prove that any circ-UMFF is a totally ordered set and a factorization over it must be monotonic. We define atom words and initiate a study of u, v-atoms. Applications of circ-UMFFs arise in string algorithmics.
ISSN:0129-0541
1793-6373
DOI:10.1142/S0129054108006133