Uniquely decodable n-gram embeddings

Leonid Kontorovich

doi:10.1016/j.tcs.2004.10.010

Uniquely decodable n-gram embeddings

Leonid Kontorovich

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

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

Original language	English
Pages (from-to)	271-284
Number of pages	14
Journal	Theoretical Computer Science
Volume	329
Issue number	1-3
DOIs	https://doi.org/10.1016/j.tcs.2004.10.010
State	Published - 13 Dec 2004
Externally published	Yes

Keywords

Embedding
Finite state automaton
Finite transducer
N-gram
String

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1016/j.tcs.2004.10.010

Cite this

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title = "Uniquely decodable n-gram embeddings",

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

keywords = "Embedding, Finite state automaton, Finite transducer, N-gram, String",

author = "Leonid Kontorovich",

note = "Funding Information: Part of this research was done at the Hebrew University of Jerusalem. The work at CMU was supported by NSF Grant EIA-0205456. ∗ Tel.: +1 412 337 4438; fax: +1 412 268 6298. E-mail address: [email protected] (L. Kontorovich). URL: http://www.cs.cmu.edu/∼lkontor/.",

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N2 - We define the family of n-gram embeddings from strings over a finite alphabet into the semimodule double struck N signK. We classify all ζ ∈ double struck N signk that are valid images of strings under such embeddings, as well as all ζ whose inverse image consists of exactly 1 string (we call such ζ uniquely decodable). We prove that for a fixed alphabet, the set of all strings whose image is uniquely decodable is a regular language.

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

KW - Embedding

KW - Finite state automaton

KW - Finite transducer

KW - N-gram

KW - String

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DO - 10.1016/j.tcs.2004.10.010

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SP - 271

EP - 284

JO - Theoretical Computer Science

JF - Theoretical Computer Science

IS - 1-3

ER -

Uniquely decodable n-gram embeddings

Abstract

Keywords

ASJC Scopus subject areas

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