Issue RAIRO-Theor. Inf. Appl. Volume 42, Number 2, April-June 2008 Page(s) 217 - 236 DOI 10.1051/ita:2007036 Published online 13 December 2007

RAIRO-Theor. Inf. Appl. 42, 217-236 (2008)
DOI: 10.1051/ita:2007036

Binary operations on automatic functions

Juhani Karhumäki¹, Jarkko Kari¹ and Joachim Kupke<sup>2

1</sup>  University of Turku, Finland; karhumak@cs.utu.fi, jkari@utu.fi
²  ETH Zurich, Switzerland; joachimk@google.com

(Received September 9, 2005. Accepted May 2, 2006. Published online 13 December 2007.)

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.

Mathematics Subject Classification. 68Q45, 68Q10, 68U10

Key words: Automatic functions -- weighted finite automata -- full Cartesian product


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