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Invertible operations on a Cellular Neural Network Universal Machine
Author(s) -
Csapodi Márton,
Vandewalle Joos,
Roska Tamás
Publication year - 1998
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/(sici)1097-007x(199811/12)26:6<611::aid-cta36>3.0.co;2-6
Subject(s) - invertible matrix , cellular automaton , binary number , computer science , boolean function , binary operation , cellular neural network , theoretical computer science , artificial neural network , function (biology) , automaton , subroutine , algorithm , mathematics , discrete mathematics , arithmetic , artificial intelligence , pure mathematics , evolutionary biology , biology , operating system
This paper is concerned with the invertibility of parallel operations definable on two‐dimensional binary arrays by means of a local Boolean function. In this way, it contributes to the theory of cellular automata and may open new potentialities to cellular neural network applications. We provide a theoretically new approach to the invertibility of two‐dimensional additive maps which can be used to obtain detailed information on the behaviour of these operations. Other ways to make invertible operations are also investigated, including local maps which are additive in only one of the terms, and second‐order cellular automata. The discussed techniques yield a rich variety of invertible operations on infinite and/or finite two‐dimensional binary arrays. When implemented on CNN Universal Chips, all of these operations, performed by TeraOPS speed, become subroutines of a 2D analogic algorithm. These operations can be used in 2D cryptography. © 1998 John Wiley & Sons, Ltd.