IJPAM: Volume 64, No. 1 (2010)

NEARMEDIA AND THEIR REPRESENTATIONS

Yotsanan Meemark$^1$, Ekkasit Sangvisut$^2$
$^{1,2}$Department of Mathematics
Faculty of Science
Chulalongkorn University
Bangkok, 10330, THAILAND
$^1$e-mail: yotsanan.m@chula.ac.th
$^2$e-mail: perfectackle@hotmail.com


Abstract.Let $\mathscr{S}$ be a nonempty set and $\mathscr{T}$ a nonempty set of functions on $\mathscr{S}$. Elements of $\mathscr{S}$ are called states and elements of $\mathscr{T}$ are called token. A token system $(\mathscr{S},\mathscr{T})$ is called a medium if it satisfies:

[$M_1$]
for any two distinct states $S$ and $T$ in $\mathscr{S}$, there is a concise message transforming $S$ into $T$, and
[$M_2$]
a message which is closed for some state is vacuous.
A nearmedium is a token system which satisfies the condition [$M_1$]. In this work, we present some families and elementary properties of nearmedia and their representations.

Received: September 18, 2009

AMS Subject Classification: 05C62, 68R10

Key Words and Phrases: media, nearmedia, token systems, graded families

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 64
Issue: 1