Problems with Left Factored Grammar
Leftfactored grammar creates an ambiguous situation for topdown parsers. Topdown parsers cannot choose the production to derive the given string since multiple productions will have a common prefix. This creates an ambiguous situation for the topdown parser.
To tackle this situation, we need to convert the leftfactored grammar into an equivalent grammar without any productions having a common prefix. This is done using left factoring in Compiler design.
Left Factoring in Compiler Design
Left factoring is used to convert a leftfactored grammar into an equivalent grammar to remove the uncertainty for the topdown parser. In left factoring, we separate the common prefixes from the production rule.
The following algorithm is used to perform left factoring in the grammar
Suppose the grammar is in the form:
A â‡’ Î±Î˛1  Î±Î˛2  Î±Î˛3  â€¦â€¦  Î±Î˛n  Îł
Where A is a nonterminal and Î± is the common prefix.
We will separate those productions with a common prefix and then add a new production rule in which the new nonterminal we introduced will derive those productions with a common prefix.
A â‡’ Î±A`
A` â‡’ Î˛1  Î˛2  Î˛3  â€¦â€¦  Î˛n
The topdown parser can easily parse this grammar to derive a given string. So this is how left factoring in compiler design is performed on a given grammar.
Benefits of Left Factoring in Compiler Design
Left factoring has multiple benefits associated with it. Some of the benefits of left factoring are
 Error Detection: With the help of left factoring, error detection becomes easier since the prefix in the input string which caused the error while parsing can now be identified easily.
 The complexity of rules is decreased: The complexity of complex and larger rules with common prefixes is decreased as we factor out the common prefix. This makes the grammar more readable, and the rules become simpler.
 Consistent Grammar: Left factoring helps make the grammar consistent since it follows predefined standards. It ensures that the grammar is welldefined and predictable.
Challenges in Left Factoring in Compiler Design
Many challenges are faced while performing left factoring in the grammar. Some of the challenges are
 Introduces ambiguity: Performing left factoring in grammar can sometimes give rise to ambiguity as it introduces new rules, making it possible for the parser to parse a string in multiple ways.
 Decrease in Parsing Efficiency: In left factoring, multiple new production rules are added by factoring out the common prefix. New nonterminals are also introduced by us. This increases the size of the grammar and hence makes it more complex.
 Identification of common prefixes: Sometimes, identifying common prefixes is difficult if the size of the grammar is already very large.
Implementation of left factoring
Let's see the implementation of left factoring with the help of an example.
The given production rule is
A â‡’ aB  aC  aD
B â‡’ b
C â‡’ c
D â‡’ d
A, B, C, and D are nonterminals, while a,b,c, and d are terminals.
We are going to separate those productions which have a common prefix. In this example, A â‡’ aB, A â‡’ aC, and A â‡’ aC are three such productions. We take the common prefix and create a new nonterminal A`.
A â‡’ aA` where A` is the new nonterminal we introduced.
We then add a new production rule in which the new nonterminal we introduced will derive those productions with a common prefix.
A` â‡’ B  C  D
Therefore the final grammar would be
A â‡’ aA`
A` â‡’ B  C  D
B â‡’ b
C â‡’ c
D â‡’ d
The topdown parser can easily parse this grammar to derive a given string. So this is how left factoring in compiler design is performed on a given grammar.
Comparison with other parsing techniques
We have seen how and why left factoring is used in our grammar. Apart from left factoring, there are other parsing techniques as well. Some of them are

LL Parsing algorithm: It is one of the topdown parsing techniques. This algorithm maintains a parsing table for the given grammar, a stack, and a parser while parsing a string. It determines whether the given grammar/parsing table can form the specified string. If it cannot be produced, then we get an error. Left factoring in compiler design can improve efficiency in LL parsing algorithms.

CYK algorithm: CYK (Chomsky Normal Form) is a basic algorithm for parsing contextfree grammar (CFG). This algorithm checks if a string can be parsed using a given grammar. Left factoring reduces the size of the parsing table so that the parsing efficiency can be increased.
 LR Parsing algorithm: LR parsing is a bottomup parsing technique for contextfree grammar. The input string is parsed from left to right, producing a rightmost derivation. It reduces the toplevel grammar productions as it builds from the leaves. Left factoring minimizes the number of states in the LR parsing table to improve efficiency.
Frequently Asked Questions
What is topdown parsing?
Topdown parsing is one of the techniques in which the parser starts with the highestlevel nonterminal symbol of the grammar and works downwards to derive the input string. It involves choosing a production rule for the current nonterminal symbol and recursively expanding it.
What is left recursion in compiler design?
Left recursion in compiler design is an unwanted situation that sometimes arises in our grammar while parsing the syntax. If there is a production rule in which a nonterminal symbol derives itself as the first symbol on the right side, it is called left recursion.
What is the difference between left recursion and left factoring in compiler design?
In leftfactored grammar, productions have a common prefix, i.e., a grammar in the form S â‡’ aX  aY  aZ. In contrast, in left recursive grammar, there is a production rule in which a nonterminal symbol derives itself as the first symbol on the right side. It will be in the form S â‡’ Sa  Ab  cb, where S is nonterminal.
Why is left factoring a problem?
Left factoring is a problem because it creates ambiguity in understanding and translating programming code. It's like having sentences that start similarly but go in different directions, confusing the translation process.
Conclusion
Congrats, Ninja!! You've learned what left factoring in compiler design is and why removing left factoring from our grammar is necessary. You have also learned how to remove it from your grammar so that it doesn't create any uncertainty for the topdown parser.
We have also added some FAQs related to the left factoring in compiler design.
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