Introduction to Discrete event system学习笔记4.9

1.A Deterministic Automaton,defined by G,is a six-tuple

　　G=(X,E,f,Γ,x₀,X_m)

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→2^E  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

　　X_m ⊆X is the set of marked states.

2.The language generated by G=(X,E,f,Γ,x₀,X_m) is

　　L(G):={s∈ E*:f(x₀,s) is defined}

　　The language marked by G is

　　L_m(G):={s∈ L(G):f(x₀,s)∈ X_m}

　　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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