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Real functions on the domain - 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 functions, weighted finite automata, full cartesian product
Karhumäki, Juhani  ; Kari, Jarkko  ; Kupke, Joachim 1
@article{ITA_2008__42_2_217_0, author = {Karhum\"aki, Juhani and Kari, Jarkko and Kupke, Joachim}, title = {Binary operations on automatic functions}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, pages = {217--236}, publisher = {EDP-Sciences}, volume = {42}, number = {2}, year = {2008}, doi = {10.1051/ita:2007036}, mrnumber = {2401259}, zbl = {1144.68034}, language = {en}, url = {http://geodesic.mathdoc.fr/articles/10.1051/ita:2007036/} }
TY - JOUR AU - Karhumäki, Juhani AU - Kari, Jarkko AU - Kupke, Joachim TI - Binary operations on automatic functions JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2008 SP - 217 EP - 236 VL - 42 IS - 2 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ita:2007036/ DO - 10.1051/ita:2007036 LA - en ID - ITA_2008__42_2_217_0 ER -
%0 Journal Article %A Karhumäki, Juhani %A Kari, Jarkko %A Kupke, Joachim %T Binary operations on automatic functions %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2008 %P 217-236 %V 42 %N 2 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ita:2007036/ %R 10.1051/ita:2007036 %G en %F ITA_2008__42_2_217_0
Karhumäki, Juhani; Kari, Jarkko; Kupke, Joachim. Binary operations on automatic functions. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 2, pp. 217-236. doi: 10.1051/ita:2007036
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