On Nilpotency and Asymptotic Nilpotency of Cellular Automata
نویسندگان
چکیده
منابع مشابه
On Nilpotency and Asymptotic Nilpotency of Cellular Automata
One of the most interesting aspects in the theory of cellular automata is the study of different types of nilpotency, that is, different ways in which a cellular automaton can force a particular symbol (usually called 0) to appear frequently in all its spacetime diagrams. The simplest such notion, called simply ‘nilpotency’, is that the cellular automaton c maps every configuration to a uniform...
متن کاملNilpotency and Limit Sets of Cellular Automata
A one-dimensional cellular automaton is a dynamical system which consisting in a juxtaposition of cells whose state changes over discrete time according to that of their neighbors. One of its simplest behaviors is nilpotency: all configurations of cells are mapped after a finite time into a given “null” configuration. Our main result is that nilpotency is equivalent to the condition that all co...
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The limit set of a celullar automaton consists of all the configurations of the automaton that can appear after arbitrarily long computations. It is known that the limit set is never empty--it contains at least one homogeneous configuration. A CA is called nilpotent if its limit set contains just one configuration. The present work proves that it is algorithmically undecidable whether a given o...
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We consider an affine control system whose vector fields span a third-order nilpotent Lie algebra. We show that the reachable set at time T using measurable controls is equivalent to the reachable set at time T using piecewise-constant controls with no more than four switches. The bound on the number of switches is uniform over any final time T . As a corollary, we derive a new sufficient condi...
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Article history: Received 13 May 2010 Accepted 1 June 2010 Available online 4 July 2010 Submitted by R.A. Brualdi AMS classification: 15A15 15A18
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ژورنال
عنوان ژورنال: Electronic Proceedings in Theoretical Computer Science
سال: 2012
ISSN: 2075-2180
DOI: 10.4204/eptcs.90.7