# 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

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topKarhumäki, 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 -

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