Table of Contents
Design Push Down Automata
Language in string formate
The language recognized by a Pushdown Automaton is known as a context-free language. A context-free language is a set of strings that can be generated by a context-free grammar. A context-free grammar consists of production rules that define how the symbols of the language can be generated. The stack in a PDA helps in keeping track of the context or structure of the language being recognized.
L= { abba, aabbbbaa,abbbbbba, …………}
this language design the Push Down Automata
PDA
define the PDA formally:
Q: Set of states
Σ: Input alphabet
Γ: Stack alphabet
δ: Transition rules
q0: Initial state
Z: Initial stack symbol
F: Set of final states
The PDA will be denoted as M = (Q, Σ, Γ, δ, q0, Z, F),
Design Push Down Automata in Diagram
Transition rule
Design Push Down Automata in text
The transition rules (δ) are as follows:
- δ(Q0, a, Z) -> (Q0, aZ)
- δ(Q0, b, Z) -> (Q0, bZ)
- δ(Q0, a, a) -> (Q0, aa) (reading ‘a’ and pushing ‘a’ onto the stack)
- δ(Q0, b, b) -> (Q0, bb) (reading ‘b’ and pushing ‘b’ onto the stack)
- δ(Q0, ε, ε) -> (Q0, ε) (reached the end of the first part ‘W’)
- δ(Q0, a, a) -> (Q1, ε) (reading ‘a’ and popping from the stack
- δ(Q0, b, b) -> (Q1, ε) (reading ‘b’ and popping from the stack)
- δ(Q1, a, a) -> (Q1, ε) (reading ‘a’ and popping from the stack
- δ(Q1, b, b) -> (Q1, ε) )(reading ‘b’ and popping from the stack
- δ(Q1, ε, Z) -> (Qf, Z) (reached the end of the second part ‘W^T’ and accepted)
In the transition rules, ε denotes an empty string, and the stack symbols ‘a’ and ‘b’ are used to keep track of the characters of the first part (W) of the string. The PDA starts in state q0 and uses the stack to compare the second part (W^T) with the first part (W) in reverse.
This PDA will accept all strings of the form WW^T, where W can be any combination of ‘a’ and ‘b’. If the input string does not belong to this language, the PDA will reach a non-final state during its execution, and the input will be rejected.
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