What is Push Down Automata in TOC?

A pushdown automaton is a machine that is capable of recognizing context-free grammar. They’re similar to automata with an additional element — a stack, which gives them more control over memory.

PDA = Finite state machine + stack

A pushdown automaton has three components −

·        an input tapes

·        a control unit

·        a stack with an infinite size

The stack head scans the top symbol of the stack.

A stack does two operations –   (1) Push      (2) POP

Push − a new symbol is added at the top.

Pop − the top symbol is read and removed.

Formally, a pushdown automaton is defined as a 6-tuple:  (Q,Σ, Γ,δ,q0, F) , with the following variable definitions:

Ø Q is a finite set of states

Ø Σ is a finite alphabet—the input

Ø Γ is a finite alphabet—the stack

Ø δ is the transition functions, with the following composition:

Q x Σ x Γ→P (Q x Γ)

Ø q₀ is the start state

Ø F is the set of accepted states ∈Q

δ : PDA will read input symbol and stack symbol (top of the stack) and move to a new state and change the symbol of the stack.

PDA is of two types:

·        Deterministic PDA (Going to only one state and pushing one element to TOS)

·        Non - deterministic PDA (Going to more than one states and print more than one element to TOS)

Application:

·        For designing the parsing phase of a compiler (Syntax Analysis).

·        For implementation of stack applications.

·        For evaluating the arithmetic expressions.

·        For solving the Tower of Hanoi Problem.

·        Understand PDA with examples

 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
• What is Two-way infinite Turing machine?
• Example to generate Parse tree from the given grammar

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