Definition of a Deterministic Finite Automaton

A deterministic finite automaton consists of:

 1.A finite set of states,often denoted Q.

 2.A finite set of input symbol,often denoted ∑.

 3.A transition function that takes as arguments a state and an input symbol
 and returns a state.The transition function will commonly be denoted δ.
 In our informal graph representation of automata, δ was represented by
 arcs between states and the labels on the arcs. If q is a state, and a is an
 input symbol, then δ(q,a) is that state p such that there is an arc labeled a from q to p.^2

 4.A start state, one of the states in Q.

 5.A set of final or accepting states F. The set F is a subset of Q.

A deterministic finite automaton will often be referred to by its acronym: DFA.
The most succinct representation of a DFA is a listing of the ve components
above. In proofs we often talk about a DFA in "five-tuple" notation:
A = (Q,Σ, δ, q0,F)
where A is the name of the DFA. Q is its set of states,∑ its input symbols,δ
its transition function,q0 its start state,and F its set of accepting states.

Components