Binary operations on automatic functions

Juhani Karhumäki; Jarkko Kari; Joachim Kupke

RAIRO - Theoretical Informatics and Applications (2007)

  • Volume: 42, Issue: 2, page 217-236
  • ISSN: 0988-3754

Abstract

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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.

How to cite

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Karhumäki, Juhani, Kari, Jarkko, and Kupke, Joachim. "Binary operations on automatic functions." RAIRO - Theoretical Informatics and Applications 42.2 (2007): 217-236. <http://eudml.org/doc/92868>.

@article{Karhumäki2007,
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. },
author = {Karhumäki, Juhani, Kari, Jarkko, Kupke, Joachim},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Automatic functions; weighted finite automata; full Cartesian product; digital images},
language = {eng},
month = {12},
number = {2},
pages = {217-236},
publisher = {EDP Sciences},
title = {Binary operations on automatic functions},
url = {http://eudml.org/doc/92868},
volume = {42},
year = {2007},
}

TY - JOUR
AU - Karhumäki, Juhani
AU - Kari, Jarkko
AU - Kupke, Joachim
TI - Binary operations on automatic functions
JO - RAIRO - Theoretical Informatics and Applications
DA - 2007/12//
PB - EDP Sciences
VL - 42
IS - 2
SP - 217
EP - 236
AB - 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.
LA - eng
KW - Automatic functions; weighted finite automata; full Cartesian product; digital images
UR - http://eudml.org/doc/92868
ER -

References

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