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Finite Automata With Outputs

 

Under finite automata we have two other machines. (a) Mealy machine and (b) Moore machine. These machines produces some output also at every state.

  1. Mealy Machine
    A mealy machine is a tuple
    (Q, Σ, Δ, δ, λ, q0) where
    Q = finite set of states
    Σ = finite non-empty set of input alphabets
    Δ = the set of output alphabets
    δ = transition function defined as Q × Σ  Q.
    λ = the output function defined as Σ × Q  Δ means at any state the value of current state and current input defines the output
    q0 = initial state

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Here, in the given mealy machine when input 0 is applied to state q0 it produces output a and when 0 is applied to state q1 it produces the output b. The transition table will be represented as
 

842.png 

In case of Mealy machine output is ^ if input is ^.

  1. Moore Machine
    Moore machine is a set of six tuples (Q Σ, Δ, λ q0) where,
    Q = set of states
    Σ = set of inputs
    Δ = set of outputs
    δ = transition function defined as Q × Σ  Q
    λ = output function defined as Q  Δ means only the current state of automata will define the output
    q0 = the initial state
    As we can illustrate the Moore machine in following example.
    Herre, q0 state will generate output a and q1 state will generate output b. The transition table will be given as

847.png 
 

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