Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Addition Machines, Automatic Functions and Open Problems of Floyd and
  Knuth   Floyd and Knuth investigated in 1990 register machines which can add,
subtract and compare integers as primitive operations. They asked whether their
current bound on the number of registers for multiplying and dividing fast
(running in time linear in the size of the input) can be improved and whether
one can output fast the powers of two summing up to a positive integer in
subquadratic time. Both questions are answered positively. Furthermore, it is
shown that every function computed by only one register is automatic and that
automatic functions with one input can be computed with four registers in
linear time; automatic functions with a larger number of inputs can be computed
with 5 registers in linear time. There is a nonautomatic function with one
input which can be computed with two registers in linear time.

34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th