元胞自动机的幂零性和渐近幂零性

AUTOMATA & JAC Pub Date : 2012-05-30 DOI:10.4204/EPTCS.90.7

Ville Salo

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引用次数: 13

摘要

元胞自动机理论中最有趣的一个方面是对不同类型的幂零性的研究，也就是说，元胞自动机可以迫使特定符号(通常称为0)在其所有时空图中频繁出现的不同方式。最简单的概念，简称为“零性”，是元胞自动机c将每个构型映射到一个一致的构型:::000:::，在这个构型上，它作为恒等，以一致有界的步数，即c

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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 typesof nilpotency, that is, different ways in which a cellular automaton can force a particular symbol (usu-ally called 0) to appear frequently in all its spacetime diagrams. The simplest such notion, called sim-ply ‘nilpotency’, is that the cellular automaton c maps every conﬁguration to a uniform conﬁguration:::000:::, on which it behaves as the identity, in a uniformly bounded number of steps, that is, c

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