# Moore Machine

Moore Machine is the important topic of the Theory Of Computation. Theory Of Computation is the Important subject of the Computer.

## Moore Machine

Mathematically Moore machine is a six-tuple machine and define as Mo=( Q, Ʃ, ∆, δ, ** _{/}**\’,q

_{0}) where

##### Q: A Nonempty finite set of state in Mo

Ʃ: A Nonempty finite set of input symbols ∆: A Nonempty finite set of outputs δ: It is transition function which takes two arguments as infinite automata, one is input state and other is input symbol. The output of this function is a single state, so clearly δ is the function which is responsible for the transition of Mo.

**/**\’: it is a mapping function which maps Q to ∆, giving the output associated with each state.

q_{0 }: Is the initial state of Mo and q_{0} ∈ Q.

**Examples of Moore Machine **

**1.Design a more machine for the 1’s complement of the binary number.****Fig – Moore M/c for 1’s compliment**

**2.Design a Moore machine to count the occurrence of “ab” as a substring.****Fig – Moore M/c to count occurrences of ab**

**3.Construct Moore machine that takes set of all strings over {0, 1} and produces ‘A’ if i/p ends witg ‘10’ or produces ‘B’ if i/p ends with ’11’ otherwise produces ‘C’.****Fig – Moore M/c for string ending in 10 or 11**

**4.Construct Moore machine that takes a binary number as an i/p and produces residue modulo ‘3’ as an output.****Table – transition Table **

**Fig – Moore M/c to produces residue modulo ‘3’**

### Mealy Machine

It is a finite automaton in which output is associated with each transition.

Moreover, Mathematically mealy machine is a six-tuple machine and define as Me=( Q,Ʃ, ∆, δ , _{/}\’,q_{0}) where Q: A Nonempty finite set of state in Me Ʃ: A Nonempty finite set of input symbols ∆: A Nonempty finite set of outputs δ: It is transition function which takes two arguments as in Moore machine, one is input state and other is input symbol. Moreover, The output of this function is a single state, so clearly δ is the function which is responsible for the transition of Me. /\’: it is a mapping function which maps Q x Ʃ to ∆, giving the output associated with each transition.q0: Is the initial state of Me and q_{0} ∈ Q. **Examples of Mealy Machine **

**Design a mealy machine for the 1’s complement of the binary number. ****Fig – Mealy M/c for 1’s compliment of binary**

**Design a mealy machine for the 1’s complement of the binary number.**

**Fig – Mealy M/c for 1’s compliment of binary****Design a mealy machine for regular expression (0+1)*(00+11). ****Fig – Mealy M/c for (0+1)*(00+11)**

**Design a mealy machine where Ʃ={0, 1, 2} print residue modulo 5 of input treated as ternary (base 3). **

**Fig – Mealy M/c to produces residue modulo ‘5’**

**Related Terms**

Theory of Computation, Definition-Finite Automata, NFA – ^ to FA, Regular language & Expression

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