Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abstract Geometrical Computation 8: Small Machines, Accumulations and
  Rationality   In the context of abstract geometrical computation, computing with colored
line segments, we study the possibility of having an accumulation with small
signal machines, ie, signal machines having only a very limited number of
distinct speeds. The cases of 2 and 4 speeds are trivial: we provide a proof
that no machine can produce an accumulation in the case of 2 speeds and exhibit
an accumulation with 4 speeds. The main result is the twofold case of 3 speeds.
On the one hand, we prove that accumulations cannot happen when all ratios
between speeds and all ratios between initial distances are rational. On the
other hand, we provide examples of an accumulation in the case of an irrational
ratio between 2 speeds and in the case of an irrational ratio between two
distances in the initial configuration. This dichotomy is explained by the
presence of a phenomenon computing Euclid's algorithm (gcd): it stops if and
only if its input is commensurate (ie, of rational ratio).

11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph