Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Uniquely Ergodic Cellular Automaton   We construct a one-dimensional uniquely ergodic cellular automaton which is
not nilpotent. This automaton can perform asymptotically infinitely sparse
computation, which nevertheless never disappears completely. The construction
builds on the self-simulating automaton of G\'acs. We also prove related
results of dynamical and computational nature, including the undecidability of
unique ergodicity, and the undecidability of nilpotency in uniquely ergodic
cellular automata.

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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg