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Compatibility relations on codes and free monoids

Published online by Cambridge University Press:  03 June 2008

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 andsymmetric relation on words of equal length. We consider these wordrelations with respect to the theory of variable length codes andfree monoids. We define an (R,S)-code and an (R,S)-free monoidfor arbitrary word relations R and S. ModifiedSardinas-Patterson algorithm is presented for testing whether finitesets of words are (R,S)-codes. Coding capabilities of relationalcodes are measured algorithmically by finding minimal and maximalrelations. We generalize the stability criterion of Schützenbergerand 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 itcan be computed. We prove a defect theorem for (R,S)-free hulls.In addition, a defect theorem of partial words is proved as acorollary.

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Type
Research Article
Copyright
© EDP Sciences, 2008

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