1. What Is CFG To CNF Conversion?

CFG to CNF conversion transforms context-free grammar rules into Chomsky normal form, where all production rules are either of the form A → BC or A → a, where A, B, C are non-terminals and a is a terminal.

2. How The Conversion Process Works

The conversion follows a multi-step algorithmic process:

Conversion Steps:

• Remove ε-productions (null productions)
• Remove unit productions (A → B)
• Replace productions with mixed terminals and non-terminals
• Break productions with more than 2 non-terminals into chains
• Ensure all productions are in proper CNF format

3. Importance Of Chomsky Normal Form

Details: CNF is important for parsing algorithms like CYK algorithm, simplifies grammar analysis, and provides a standardized form for theoretical computer science applications.

4. Using The Calculator

Tips: Enter your context-free grammar rules in the text area. Each rule should be on a separate line using standard notation (e.g., S → aB | bA).

5. Frequently Asked Questions (FAQ)

Q1: What input format should I use for CFG rules?
A: Use standard notation with one production per line, using → or -> for production arrows and | for alternatives.

Q2: Does every CFG have an equivalent CNF?
A: Yes, every context-free grammar without ε-productions (except possibly S → ε) has an equivalent CNF.

Q3: What are the main benefits of CNF?
A: CNF simplifies parsing, enables efficient algorithms like CYK, and provides a standardized form for grammar analysis.

Q4: Are there limitations to CNF conversion?
A: The conversion process may significantly increase the number of production rules and non-terminal symbols in the grammar.

Q5: Can CNF handle empty string productions?
A: Only the start symbol can produce the empty string (if the language contains ε), and this must be handled as a special case.