ThmDex – An index of mathematical definitions, results, and conjectures.
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State machine
Definition D3495
Finite state machine
Formulation 0
A D5815: Quintuple $(Q, \Sigma, \delta, q_0, F)$ is a finite state machine if and only if
(1) $Q \neq \emptyset$ is a D17: Finite set (of states)
(2) $\Sigma \neq \emptyset$ is a D17: Finite set (the input alphabet)
(3) $\delta : Q \times \Sigma \to Q$ (the word transition function)
(4) $q_0 \in Q$ (the initial state)
(5) $F \subseteq Q$ is a D2115: Nonempty set (of final or halting or accepting states)