Uniquely decodable n-gram embeddings

Authors:
Leonid Kontorovich
Affiliations:
Center for Automated Learning and Discovery, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA
Venue:
Theoretical Computer Science
Year:
2004

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Abstract

We define the family of n-gram embeddings from strings over a finite alphabet into the semimodule NK. We classify all ξ ∈ NK that are valid images of strings under such embeddings, as well as all ξ whose inverse image consists of exactly 1 string (we call such ξ uniquely decodable). We prove that for a fixed alphabet, the set of all strings whose image is uniquely decodable is a regular language.