Concept on Moore Machine

Finite automata and finite state machines got a complete form by the efforts of George H. Mealy at the Bell Labs and Edward F. Moore in IBM around 1960.

Basically, Finite state machines are divided into two parts

(1) Automata without Output

(2) Automata with Output.

The machines with output are named Mealy and Moore machines. These machines are either dependent on their present states and present input or only in the Present state only. So let we discuss both in detail.

In Moore machine, outputs are unconditional (not directly dependent on the input signal) means it works on the concept of one state - one output means outputs are only dependent on the current state. Even without any transitions, the initial state also has output. That's the reason why Moore's machine can respond to empty strings. But if we talk about the Mealy machine it works on the concept of one transition-one output means outputs are dependent on both current state and current inputs. These are common circuit architecture, used in counters and even parity calculators.

A simple day-to-day example shared by my faculty would like to share here for a better understanding of Moore and Mealy Machine will be understood as "a person eating food without following a diet chart (Moore machine)" and "a person eating food by following the diet chart (Mealy machine)".

1) The Moore-person will eat without knowing his body's requirements. This means he will not think of eating anything depending upon what he has eaten or what his body requires at the current state.

2) Whereas, the Mealy-person would rather follow a diet and eat accordingly i.e following his current body requirement.

A Moore machine is defined by the six tuple      

                                                M = (Q, Σ, Γ, δ, θ, q0),

Where

Q is a finite set of internal states,
Σ is the input alphabet,
Γ is the output alphabet,
δ : Q × Σ → Q is the transition function,
θ : Q → Γ is the output function,
q0 ∈ Q is the initial state.

The machine starts in state q0, at which time all input is available for processing. If at time t_n the Moore machine is in state qi, the current input symbol is a, and δ(qi, a) = qj, θ(qj) = b, the machine will enter state qj and produce output b.

In the transition graph of a Moore machine, each vertex now has two labels: the state name and the output symbols associated with the state.

Example to understand Moore machine

 Also, Study about: 

• Mealy Machine
• Moore Machine
• Rice Theorem
• Brief about Turing Machine
• Multi Dimension Turing Machine
• Multiple Turing Machine
• Parikh Theorem in TOC
• Parse Tree or Derivation Tree
• What do you Understand by Derivation
• MyHill Nerode Theorem
• Minimize Myhill Nerode Theorem
• Push Down Automata
• Know Where we use Automata
• What do you understand by Derivation of Grammar
• What is Context-free Grammar
• Example based on CFG
• Regular Expression in TOC

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