Name
Abstract | ||
|---|---|---|
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. |
Year | Venue | Keywords |
|---|---|---|
2010 | Clinical Orthopaedics and Related Research | discrete mathematics,normal form,satisfiability |
Field | DocType | Volume |
Discrete mathematics,Combinatorics,Associative property,Power associativity,Monoid,Confluence,Rewriting,Syntactic monoid,Free monoid,Trace theory,Mathematics | Journal | abs/1002.2 |
Issue | ISSN | Citations |
2 | Journal of Pure and Applied Mathematics 3, 2 (2010) 265-285 | 0 |
PageRank | References | Authors |
0.34 | 7 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Laurent Poinsot | 1 | 33 | 7.32 |
| Gerard H. E. Duchamp | 2 | 2 | 1.09 |
| Christophe Tollu | 3 | 126 | 57.12 |