Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computability of the entropy of one-tape Turing Machines   We prove that the maximum speed and the entropy of a one-tape Turing machine
are computable, in the sense that we can approximate them to any given
precision $\epsilon$. This is contrary to popular belief, as all dynamical
properties are usually undecidable for Turing machines. The result is quite
specific to one-tape Turing machines, as it is not true anymore for two-tape
Turing machines by the results of Blondel et al., and uses the approach of
crossing sequences introduced by Hennie.

32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con