Radix Cross-Sections for Length Morphisms

We prove that the radix cross-section of a rational set for a length morphism, and more generally for a rational function from a free monoid into N, is rational, a property that does not hold any more if the image of the function is a subset of a free monoid with two or more generators. proceedings short version1 The purpose of this paper is to give a positive answer to a problem left open in an old paper by the second author ([11]) and to prove the following property, a refinement of the Cross-Section Theorem ([3]):

• Type: Conference
• Year: 2010
• Where: LATIN
• Authors: Sylvain Lombardy, Jacques Sakarovitch
• Keywords: Free Monoid, Information Retrieval, LATIN 2010, Rational Function, Rational Set