A Survey of Microcellular Research
Journal of the ACM (JACM)
A unifying framework for the theory of iterative arrays of machines
STOC '69 Proceedings of the first annual ACM symposium on Theory of computing
A parallel-acting iterative automaton
FOCS '67 Proceedings of the 8th Annual Symposium on Switching and Automata Theory (SWAT 1967)
The constructibility of a configuration in a cellular automaton
Journal of Computer and System Sciences
A completeness property of one-dimensional tessellation automata
Journal of Computer and System Sciences
Completeness problem of one-dimensional binary scope-3 tessellation automata
Journal of Computer and System Sciences
Decision procedures for surjectivity and injectivity of parallel maps for tessellation structures
Journal of Computer and System Sciences
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This report deals with the question of whether or not, for a given tessellationautomaton, there exists a finite pattern that cannot evolve from a given primitive pattern no matter what sequence of environmental input transformations are applied. This is closely related to Moore's Garden-of-Eden problem. We begin dealing with this question for the simplest nontrivial tessellation automata, namely, one-dimensional binary scope-n tessellation automata. We show that any finite pattern can evolve from the primitive pattern if the neighborhood scope is four or more. We show that there are finite patterns that cannot evolve from the primitive pattern for the scope-two case. Although some partial results are presented, the question is still open for the scope-three case. Some results for more general tessellation automata are also discussed.