1.A Deterministic Automaton,defined by G,is a six-tuple
G=(X,E,f,Γ,x0,Xm)
where:
X is the set of states
E the finite set of events associated with G
f:X×E→X is the transition function:f(x,e)=y means that there is a transition labeled by event e from state x to state y;in general,f is a partial function on its domain
Γ:X→2E is the active event function(or feasible event functiion);Γ(x) is the set of all events e for which f(x,e) is defined and it is called the active event set(or feasible event set)of G at x.
x0 is the initial state
Xm ⊆X is the set of marked states.
2.The language generated by G=(X,E,f,Γ,x0,Xm) is
L(G):={s∈ E*:f(x0,s) is defined}
The language marked by G is
Lm(G):={s∈ L(G):f(x0,s)∈ Xm}
The above definitions assume that we are working with the extended transition function f:X×E*→X. An immendiate consequece is that for any G with non-empty X.ε∈L(G).
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