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Explain the balancing parenthesis of PDA
Pushdown Automata (PDA) are the finite automata (FAs), but with the ability to push and pop symbols to/from a stack.
PDA accepts strings if there is a legal path from start state to acceptance state for input. Otherwise, the string is rejected.
A PDA can be represented by a 7-tuple
(Q, ∑, ℾ, q0, ha, ∆,δ)
Where
The PDA is to finite subsets of Q ☓ (ℾ ∪ {∆})*.
Parentheses are balanced if
- While reading string, number of opening parentheses >= number of closing parentheses.
- When string is read, number of opening parentheses = number of closing parentheses.
Examples
- (())() − Balanced
- ((()() − Not balanced
- )()(() − Not balanced
The context free grammar (CFG) is as follows −
S -> (S) | SS | ε
PDA for balancing brackets
Each (is pushed, each) causes an (to be popped). This is shown below
Updated on: 16-Jun-2021
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