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Presented By: GauravSinha

ObjectivesWhat is Automata or Automation

Theory?

How could we find output of Finite

Automata?

The Moore machine

The Mealy machine

What is Automata or Automation Theory?

• Automata Theory is the study of “Abstract machines” or It is the study of “Self-Operating virtual machines” to help in logical understanding of how input and output process in computationproblems. Automata comes from Greek word means “Self-Acting”.

• Automata are used in the field of Artificial Intelligence, computational theory, compiler design, parsing, etc.

• An Automation is supposed to run in some given sequence of inputs in Discrete time steps.

• The Automation consists of states(represents by circles) and transitions(represent by arrows)

• The figure shows how a Automation machine works :

Example of Automation

1 1

0

0

S1 S2

• An Automation contains finite number of states, as in above figure you can see S1 and S2 are two states.

• Transition of input is shown by arrow from one states to another.

• At each time step when the automation reads a symbol, it jumps or transitions to another state .

• Once all inputs has been read, the automation said to have stopped and that state is called final state.

Mathematical Representation of Finite Automation

• A deterministic finite automation is represented by a 5-tuple(Q, Σ,δ,q0,F).

• Where, Q is a finite set of states.

• Σ=finite set of symbols, called alphabets of Automation.

• δ=transition function, δ: Q* Σ Q.

• q0= start state before input is processed

• F=set of states of Q called accept states.

How could we find output of Finite Automata?

• There are two different Models to find out the output of finite-state machine

• Firstly, When output values are determined by its current state, i.e., with the help of Moore machine models.

• Secondly, when output values are determined both by its current state and by the value of its inputs, which is represented by Mealy machine model.

Moore Machine:• A Moore Machine is based on Sequential

Machines. Mathematically it can be defined using a 6-tuple (S, S0, I, Δ, δ, λ), where:

• S=Finite set of states.• S0=Start or called as Initial state.• I = Finite Set of Input Alphabet.• Δ= Finite Set of Output Alphabet.• δ = Transition function from I*S into S.• λ = Output function mapping S into Δ.Application : It is used in Edge detector, Binary

Adding machine, Clocked Sequential System, LED’s, etc.

Visual Representation:

Table

State transition table is a table showing relation between an input and a state. We can make the table of any diagram

and we can easily find out the output of finite state machine.

States a b Output

q0 q1 q2 1

q1 q1 q1 0

q2 q1 q0 1

Mealy Machine• Machine is a Six tuple(S, I, Δ, δ, λ’, S0),

where:

• S=Finite set of States.

• I = Input alphabet.

• Δ = Output alphabet.

• δ = Transition function I * S into S

• λ'= Output function mapping S into Δ.

• S0 = Initial state.

Application of Mealy Machine: Traffic lights, Bar Code Scanner, Gas Pump, Vending machine, etc.

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• Simple Mealy Machine Diagram:

State Diagram for a simple Mealy Machine with one Input and one Output.

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Si

S1

S0

SummaryBoth Moore and Mealy Machines

are used in the field of Technology. There is subtle

difference in the behaviour of a Mealy and Moore machine. Both are used to implement Simple as

well as Complex Problem of Computation in our daily life, like in

Computer, Traffic lights, LED’s, Electronic Circuits, etc.

Thank You