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Compatibility relations on codes and free monoids

Published online by Cambridge University Press:  03 June 2008

Tomi Kärki
Tomi Kärki*
Affiliation:
Department of Mathematics and Turku Centre for Computer Science, University of Turku, 20014 Turku, Finland; topeka@utu.fi
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Abstract

A compatibility relation on letters induces a reflexive and symmetric relation on words of equal length. We consider these word relations with respect to the theory of variable length codes and free monoids. We define an (R,S)-code and an (R,S)-free monoid for arbitrary word relations R and S. Modified Sardinas-Patterson algorithm is presented for testing whether finite sets of words are (R,S)-codes. Coding capabilities of relational codes are measured algorithmically by finding minimal and maximal relations. We generalize the stability criterion of Schützenberger and Tilson's closure result for (R,S)-free monoids. The (R,S)-free hull of a set of words is introduced and we show how it can be computed. We prove a defect theorem for (R,S)-free hulls. In addition, a defect theorem of partial words is proved as a corollary.

Keywords

Compatibility relationfree monoidstabilitydefect theorempartial word.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 42 , Issue 3: JM'06 , July 2008 , pp. 539 - 552
Copyright
© EDP Sciences, 2008

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