Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Growth of Replacements   The following game in a similar formulation to Petri nets and chip-firing
games is studied: Given a finite collection of baskets, each has an infinite
number of balls of the same value. Initially, a ball from some basket is chosen
to put on the table. Subsequently, in each step a ball from the table is chosen
to be replaced by some $2$ balls from some baskets. Which baskets to take
depend only on the ball to be replaced and they are decided in advance. Given
some $n$, the object of the game is to find the maximum possible sum of values
$g(n)$ for a table of $n$ balls.
  In this article, the sequence $\{g(n)/n\}_{n=1}^\infty$ will be shown to
converge to a growth rate $\lambda$. Furthermore, this value $\lambda$ is also
the rate of a structure called pseudo-loop and the solution of a rather simple
linear program. The structure and the linear program are quite closely related,
e.g. the solution of the linear program gives a pseudo-loop with the rate
$\lambda$ in linear time of the number of baskets. A method to test in
quadratic time whether a given $\lambda_0$ is smaller than $\lambda$ is
provided to approximate $\lambda$. Four proofs of the limit $\lambda$ are
given: one just uses the relation between the functions, one uses pseudo-loops,
one uses the linear program and one uses Fekete's lemma (the latest proof
assumes a condition on the rule of replacements).

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The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg