Master DFA Construction: Examples & Step-by-Step Solutions | Automata Theory 📘

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Deterministic Finite State Automata (DFA)
One-way, infinite tape, broken into cells
One-way, read-only tape head.
Finite control, i.e., a program, containing the position of the read head, current symbol being scanned, and the current “state.”
A string is placed on the tape, read head is positioned at the left end, and the DFA will read the string one symbol at a time until all symbols have been read. The DFA will then either accept or reject.

A DFA is a five-tuple:

M = (Q, Σ, δ, q0, F)

Q A finite set of states
Σ A finite input alphabet
q0 The initial/starting state, q0 is in Q
F A set of final/accepting states, which is a subset of Q
δ A transition function, which is a total function from Q x Σ to Q

δ: (Q x Σ) to Q δ is defined for any q in Q and s in Σ, and
δ(q,s) = q’ is equal to some state q’ in Q, could be q’=q

Intuitively, δ(q,s) is the state entered by M after reading symbol s while in state q.

it necessary for a dfa to have to have atleast one final state?

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