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On the structure of the set of reversible cellular automata
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I. V. Kucherenko
Published/Copyright:
December 10, 2007
We investigate the structure of the set of reversible cellular automata. In the class of two-dimensional binary linear cellular automata with variable structure, the classes with decidable and undecidable reversibility property are separated, which contain almost all such cellular automata. With the use of this result, we prove undecidability of reversibility in the class of cellular automata with Γ-pattern and sixteen states of a cell and in the class of two-dimensional binary cellular automata with self-dual local transition functions. The complete description is given for the structure of the set of reversible cellular automata of the class of binary cellular automata with local transition functions from the Post classes.
Received: 2005-November-22
Published Online: 2007-12-10
Published in Print: 2007-12-11
© de Gruyter
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Articles in the same Issue
- The limit distribution of the size of a giant component in an Internet-type random graph
- On conditions for emergence of a giant tree in a random unlabelled forest
- On the transition of distributions of sums of random variables related to the generalised allocation scheme from one lattice to another
- A multiple optimal stopping rule for sums of independent random variables
- The cycle structure of a random nonhomogeneous hypergraph on the subcritical stage of evolution
- On the structure of the set of reversible cellular automata
- On-line algorithms for packing rectangles into several strips
- An enhanced algorithm to search for low-degree annihilators for a Zhegalkin polynomial
