Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
What is Non-Immediate Left Recursion in compiler design?
A Grammar G (V, T, P, S) is left recursive if it has a production in the form.
A → A α |β.
The above Grammar is left recursive because the left of production is occurring at a first position on the right side of production. It can eliminate left recursion by replacing a pair of production with
A → βA′
A → αA′|ϵ
The general form for left recursion is
A → Aα1|Aα2| … . |Aαm|β1|β2| … . . βn
can be replaced by
A → β1A′|β2A′| … . . | … . . |βnA′
A → α1A′|α2A′| … . . |αmA′|ε
In the following grammar, it does not have the immediate or direct left recursion. But here, it can have non-immediate left recursion.
S → Ab
A → Sc|d
Here, S is left Recursive, because S ⇒ A b ⇒ S c b
Algorithm to Remove Left-Recursion
Input − Grammar G with no cycles or ε − productions.
Output − Equivalent Grammar with no Left Recursion.
Method
Order the non-terminals as A1, A2, … … … . . An
for i = 1 to n
{
for j = 1 to i – 1
{
replace each production Ai → Ajγ
by productions Ai → δ1γ| δ2γ| … … . . |δKγ
where Aj → δ1|δ2| … … . |δK
}
Remove immediate left Recursion among Ai productions.
}Example1 − Remove or Eliminate Left Recursion from the following Grammar.
S → Ab
A → Sc | d
Solution
These productions don’t have immediate left Recursion. So it cannot be eliminated directly. We can use the algorithm here to remove Left Recursion.
Step1 − Order the non-terminals S, A as A1, A2i.e., Mark S =A1, A = A2
Substituting values
∴ A1 → A2b …………… (1)
A2 → A1c|d …………… (2)
Step2 − Put values of (1) in (2)
∴ A1 → A2b
A2 → A1bc|d
Step3 − Again substitutes A1 = S and A2 = A
∴ S → A b ……………. (3)
A → A b c | d ……………. (4)
Step4 − Remove Immediate Left recursion in A → A b c | d
So,
Example2 − Remove left recursion from the following Grammar.
S → Aa |b
A → Ac | Sd|e
Solution
As we don’t have immediate left recursion so, we have to apply the algorithm here.
Step1 − Rename S, A as A1, A2 respectively.
A1 → A2 a | b …………… (1)
A2 → A2c | A1d|e ……………. (2)
Step2 − Substitute value of A1 of the statement (1) in R.H.S of the statement (2).
A1 → A2 a | b
A2 → A2 c |A2 a d|bd|e.
Step3 − Again, substitute A1 = S, A2 = A
S → Aa |b …………….. (3)
A → Ac |A a d|bd|e ……………… (4)
Step4 − Statement (4) has an immediate left recursion. Removing immediate left recursion we get
971 Views
