Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Subtraction makes computing integers faster   We show some facts regarding the question whether, for any number $n$, the
length of the shortest Addition Multiplications Chain (AMC) computing $n$ is
polynomial in the length of the shortest division-free Straight Line Program
(SLP) that computes $n$.
  If the answer to this question is "yes", then we can show a stronger upper
bound for $\mathrm{PosSLP}$, the important problem which essentially captures
the notion of efficient computation over the reals. If the answer is "no", then
this would demonstrate how subtraction helps generating integers
super-polynomially faster, given that addition and multiplication can be done
in unit time.
  In this paper, we show that, for almost all numbers, AMCs and SLPs need same
asymptotic length for computation. However, for one specific form of numbers,
SLPs are strictly more powerful than AMCs by at least one step of computation.

16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys