ABSTRACT
Let G = (V,E) be a graph, and let Alg(G)1 = Alg(G) U {1} denote its graph algebra with the identity element 1 adjoined. We take a subset T of Alg(G) U {1}, an arbitrary mapping /: X —► Alg(G) U {1}, and define the following right automaton Atmr(G,T):
• the set of states of Atmr(G,T) is V(G) U {1};
• 1 is the initial state;
• T is the set of terminal states;
• the next-state function is given by a x = a f(x ), for all a G V (G)U{1},
Hence the eventual-state function is defined by
a • (x xx2 •••«!») = (••• {(a>f(xi))f(x2) ) . . . )/(s»),
for a € Alg(G)1 and x i ,x 2, . . . ,x n £ X. The transition diagram of this automaton is a labeled Cayley graph of Alg(G).
