Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reversibility of additive CA as function of cylinder size   Additive CA on a cylinder of size $n$ can be represented by 01-string $V$ of
length $n$ which is its rule. We study a problem: a class $S$ of rules given,
for any $V\in S$ describe all sizes $n', n'>n,$ of cylinders such that
extension of $V$ by zeros to length $n'$ represents reversible additive CA on a
cylinder of size $n'$. Since all extensions of $V$ have the same collection of
positions of units, it is convenient to say about classes of collections of
positions instead of classes of rules. A criterion of reversibility is proven.
The problem is completely solved for infinite class of "block collections",
i.e. $\{(0,1,\dots,h)|h\in\mathbb Z^+\}$. Results obtained for "exponential
collections" $\{(1,2,4,\dots,2^h)|h\in\mathbb Z^+\}$ essentially reduce the
complexity of the problem for this class. Ways to transfer the results on other
classes of rules/collections are described. A conjecture is formulated for
class $\{(0,1,2^m)|m\in\mathbb Z^+\}$.

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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol