Abstract
Let E + be the space of right-half infinite sequences with entries in Z 2 and let Q be the global transition rule for the one dimensional cellular automaton ( Q, E +) for which E + is the state space. The predecessor problem for ( Q, E +) is to find all solutions of the equation Q( μ)= β where β is an arbitrary element of E +. In this paper we consider the case in which the operator Q represents an additive rule. The predecessor equation is solved in closed form for all two- and three-site rules, in particular for rules 90 and 150, and a technique is introduced which generates a closed form solution for many-higher site values. This is demonstrated with several examples.
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