Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Partial monoids: associativity and confluence   A partial monoid $P$ is a set with a partial multiplication $\times$ (and
total identity $1_P$) which satisfies some associativity axiom. The partial
monoid $P$ may be embedded in a free monoid $P^*$ and the product $\star$ is
simulated by a string rewriting system on $P^*$ that consists in evaluating the
concatenation of two letters as a product in $P$, when it is defined, and a
letter $1_P$ as the empty word $\epsilon$. In this paper we study the profound
relations between confluence for such a system and associativity of the
multiplication. Moreover we develop a reduction strategy to ensure confluence
and which allows us to define a multiplication on normal forms associative up
to a given congruence of $P^*$. Finally we show that this operation is
associative if, and only if, the rewriting system under consideration is
confluent.

35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
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The categories of this paper are: atom-ph