Formal desrciption of DFA operation

State the Formal desrciption of DFA operation ?

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A deterministic finite automaton

M = (Q, Σ, δ, q0, F)

accepts a string

w = w1 w2 w3 …wn ε Σ*

if ∃ a sequence r0, r1, r2,…, rn of states for which

–r0 = q0
–δ(ri, wi+1) = ri+1 for i = 0, 1, 2, …, n-1
–rn ∈ F

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