Start state q 0: (not shown in the examples below). In the diagram representing this FA, this is represented by an edge labeled by a pointing from the vertex labeled by q to the vertex labeled by p. Item δ(q,a)= p in the definition of the FA means that from the state named q under input symbol a, the transition to the state p occurs in this machine. This is written mathematically as δ : Q × Σ → Q, so δ (the transition function) in the definition of the FA is given by both the pair of vertices connected by an edge and the symbol on an edge in a diagram representing this FA. This mapping describes the state transition that is to occur on input of a particular symbol. An edge is usually drawn as an arrow directed from the present state to the next state.
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