Commuting Cellular Automata
نویسندگان
چکیده
The algebraic conditions under which two one-dimensional cellular automata can commute is studied. It is shown that if either rule is permutive, that is, one-to-one in its leftmost and rightmost inputs, then the other rule can be written in terms of it; if either rule is a group, then the other is linear in it; and if either is permutive and affine, that is, linear up to a constant, then the other must also be affine. We also prove some simple results regarding the existence of identities, idempotents (quiescent states), and zeroes (absorbing states).
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ورودعنوان ژورنال:
- Complex Systems
دوره 11 شماره
صفحات -
تاریخ انتشار 1997