NDLI: Continuity of Inverse Transition Relations of 2-Neighborhood Cellular Automata

Content Provider	IEEE Xplore Digital Library
Author	Ishida, T. Inokuchi, S.
Copyright Year	2013
Description	Author affiliation: Center for Fundamental Educ., Kyushu Sangyo Univ., Japan (Ishida, T.) \|\| Fac. of Math., Kyushu Univ., Fukuoka, Japan (Inokuchi, S.)
Abstract	In this paper, we discuss the continuousness of inverse transition relations of cellular automata. Generally, the inverse of a function is a relation and is not always a function. Our interest here lies in the inverse transition systems of cellular automata and cellular automata with transition relations, that is, non-deterministic cellular automata. Richardson investigated non-deterministic cellular automata and proved Richardson's theorem. The theorem provides necessary and sufficient conditions for a transition system to be a cellular automaton, and the continuousness of the transition relation is one of the conditions. We prove that the inverse relation of the transition functions of any 2-neighborhood deterministic cellular automata are continuous, and that for 2-neighborhood cellular automata of which the transition relation does not satisfy the totality, its inverse relation is not always continuous. We show an example that the transition system of the continuous inverse transition relation of a cellular automaton is not a cellular automaton.
Starting Page	495
Ending Page	499
File Size	481093
Page Count	5
File Format	PDF
e-ISBN	9781479927968
DOI	10.1109/CANDAR.2013.88
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-12-04
Publisher Place	Japan
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Inverse transition system Continuity
Content Type	Text
Resource Type	Article

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