Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: No Tits alternative for cellular automata   We show that the automorphism group of a one-dimensional full shift (the
group of reversible cellular automata) does not satisfy the Tits alternative.
That is, we construct a finitely-generated subgroup which is not virtually
solvable yet does not contain a free group on two generators. We give
constructions both in the two-sided case (spatially acting group $\Z$) and the
one-sided case (spatially acting monoid $\N$, alphabet size at least eight).
Lack of Tits alternative follows for several groups of symbolic (dynamical)
origin: automorphism groups of two-sided one-dimensional uncountable sofic
shifts, automorphism groups of multidimensional subshifts of finite type with
positive entropy and dense minimal points, automorphism groups of full shifts
over non-periodic groups, and the mapping class groups of two-sided
one-dimensional transitive SFTs. We also show that the classical Tits
alternative applies to one-dimensional (multi-track) reversible linear cellular
automata over a finite field.

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The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
3
The categories of this paper are: physics
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The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: stat