Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Immunity and Pseudorandomness of Context-Free Languages   We discuss the computational complexity of context-free languages,
concentrating on two well-known structural properties---immunity and
pseudorandomness. An infinite language is REG-immune (resp., CFL-immune) if it
contains no infinite subset that is a regular (resp., context-free) language.
We prove that (i) there is a context-free REG-immune language outside REG/n and
(ii) there is a REG-bi-immune language that can be computed deterministically
using logarithmic space. We also show that (iii) there is a CFL-simple set,
where a CFL-simple language is an infinite context-free language whose
complement is CFL-immune. Similar to the REG-immunity, a REG-primeimmune
language has no polynomially dense subsets that are also regular. We further
prove that (iv) there is a context-free language that is REG/n-bi-primeimmune.
Concerning pseudorandomness of context-free languages, we show that (v) CFL
contains REG/n-pseudorandom languages. Finally, we prove that (vi) against
REG/n, there exists an almost 1-1 pseudorandom generator computable in
nondeterministic pushdown automata equipped with a write-only output tape and
(vii) against REG, there is no almost 1-1 weakly pseudorandom generator
computable deterministically in linear time by a single-tape Turing machine.

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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: math
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The categories of this paper are: ao-sci
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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: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: alg-geom