Cellular automata machines: a new environment for modeling
Cellular automata machines: a new environment for modeling
Ininvertible cellular automata: a review
Physica D
Reversibility and surjectivity problems of cellular automata
Journal of Computer and System Sciences
On one-dimensional quantum cellular automata
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Logical reversibility of computation
IBM Journal of Research and Development
Intrinsically Universal One-dimensional Quantum Cellular Automata in Two Flavours
Fundamenta Informaticae - Machines, Computations and Universality, Part II
Intrinsically universal n-dimensional quantum cellular automata
Journal of Computer and System Sciences
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We study the family of structurally reversible cellular automata that use the (generalized) Margolus neighborhoods. We show that every reversible cellular automaton (RCA) can be embedded into the standard two layer Margolus neighborhood defined by two overlapping square partitions of the cellular space and two one-to-one local rules. The embedding allows step-by-step simulations. Then we investigate how many layers of one-to-one local rules are required in exact representations of RCA. We show how in the d-dimensional cellular space any consecutive d + 2 layers can be combined into d + 1 layers. This proves that no more than d + 1 layers are necessary. We demonstrate that in the two-dimensional case d = 2 the number d + 1 is optimal by providing an example of an RCA with three layers of local rules that cannot be expressed in two layers.