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Showing papers on "Continuous automaton published in 1977"


Book ChapterDOI
Calvin C. Elgot1
05 Sep 1977

6 citations


Journal Article
TL;DR: The classical definitions of cellular automata are modified, and the notion of finite, inhomogeneous cellular automaton is introduced, with the result: only very simple reversible cellular Automata exist in this special case.
Abstract: Cellular automata are highly parallel working systems, so they have high importance in computational applications (for example sorting [4], matrix operations, etc.). It seems difficult to apply the classical infinite, homogeneous cellular automata to these purposes [1], [2]. For this reason the classical definitions are modified in this work. In point 1. we introduce the notion of finite, inhomogeneous cellular automaton. The reason of first modification (using by many authors, e.g. [7]) is clear: only finite automaton is realisable in practice. Further the second modification (the inhomogeneity) makes the cellular automaton more flexible [11], without excluding the homogeneity in hardware [3]. In the theory of cellular automata there is a very important and interesting question, that how appear the characteristics of local maps in the global map, and conversely. This is the basic conception of present work too, having in the centre the problem of reversibility. This subject has been investigated by many authors (in particular by T. Toffoli [8], [9]), but always in the global sense. In this context the reversibility is equivalent to the bijectivity of global map. To the contrary, we mean the reversibility in local sense: a cellular automaton we shall call reversible, if its local maps may be changed so, that the new global map is the inverse of the original one. The bijectivity of global map forms necessary condition for our \"strong reversibility\". Therefore in point 2. a connection will be proved between the local maps and the number of eden-configurations, f rom which derives a necessary condition for bijectivity (it is the generalization of results in [5]). In point 3. a necessary and sufficient condition is presented to the reversibility. With this criterion we can decide the reversibility of a given cellular automaton, and construct its reverse. The point 4. contains concrete investigations in case of one-dimensional cellular automaton, with the result: only very simple reversible cellular automata exist in this special case.

2 citations


Journal ArticleDOI
TL;DR: A finite state probabilistic automaton existed that would accept a context sensitive language that is not context free and this automaton is constructed.
Abstract: It is known that nonregular languages can be accepted by finite state probabilistic automata. For many years it was not known whether a finite state probabilistic automaton existed that would accept a context sensitive language that is not context free. Such a finite state probabilistic automaton is constructed.

2 citations