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Binary operations on automatic functions

Published online by Cambridge University Press:  13 December 2007

Juhani Karhumäki ,
Jarkko Kari  and
Joachim Kupke
Juhani Karhumäki
Affiliation:
University of Turku, Finland; karhumak@cs.utu.fi, jkari@utu.fi
Jarkko Kari
Affiliation:
University of Turku, Finland; karhumak@cs.utu.fi, jkari@utu.fi
Joachim Kupke
Affiliation:
ETH Zurich, Switzerland; joachimk@google.com
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Abstract

Real functions on the domain [0,1)n – often used to describe digital images – allow for different well-known types of binary operations. In this note, we recapitulate how weighted finite automata can be used in order to represent those functions and how certain binary operations are reflected in the theory of these automata. Different types of products of automata are employed, including the seldomly-used full Cartesian product. We show, however, the infeasibility of functional composition; simple examples yield that the class of automatic functions (i.e., functions computable by automata) is not closed under this operation.

Keywords

Automatic functionsweighted finite automatafull Cartesian product
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 42 , Issue 2 , April 2008 , pp. 217 - 236
Copyright
© EDP Sciences, 2007

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