$\Delta$ is the output alphabet and $\lambda$ is a mapping from $Q$ to $\Delta$ giving the output associated with each state.Ī Mealy machine is also a six-tuple $M = (Q, \Sigma, \Delta, \delta, \lambda, q_o)$, where all is as in the Moore machine, except that $\lambda$ maps $Q \times \Sigma$ to $\Delta$. That is, $\delta(q, a)$ is a state for each state $q$ and input symbol $a$.Ī Moore machine is a six-tuple $(Q, \Sigma, \Delta, \delta, \lambda, q_o)$, where $Q$, $\Sigma$, $\delta$ and $q_0$ are as in the DFA. We formally denote a finite automaton by a 5-tuple $(Q, \Sigma, \delta, q_0, F)$, where $Q$ isĪ finite set of states, $\Sigma$ is a finite input alphabet, $Q_0$ in $Q$ is the initial state, $F \subseteq Q$ is the set of final states, and $\delta$ is the transition function mapping $Q \times \Sigma$ to $Q$. In Ullman's Introduction to Automata, Languages and Computation (1979):
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