Greibach Normal Form & CFG to GNF Conversion
Neso Academy
13 min, 17 sec
The video explains the concept of Greibach normal form and outlines the steps to convert a context-free grammar (CFG) to Greibach normal form.
Summary
- The Greibach normal form is introduced as a CFG where productions are of the form A -> b or A -> bC1C2...Cn, with A, C1...Cn as non-terminals and b as a terminal.
- Step-by-step instructions are given for converting a given CFG to Greibach normal form, including checking and removing unit/null productions, converting to Chomsky normal form if necessary, changing variable names, and ordering non-terminals.
- An example CFG is used to demonstrate the conversion process, highlighting the importance of maintaining a specific order among non-terminal symbols.
- A problematic production involving left recursion is identified, and it is mentioned that the resolution of left recursion will be covered in the next lecture.
Chapter 1
The video begins with an introduction to Greibach normal form and its significance in CFGs.
- Greibach normal form is defined, and its two acceptable production forms are explained.
- Productions should be either a non-terminal yielding a terminal or a non-terminal yielding a terminal followed by a series of non-terminals.
Chapter 2
The instructor outlines the steps required to convert a CFG to Greibach normal form.
- Check for and remove any unit or null productions from the given CFG.
- Ensure the CFG is in Chomsky normal form, converting it if it is not.
- Rename non-terminal symbols in ascending order based on their appearance in productions.
Chapter 3
An example CFG is provided to demonstrate the conversion steps to Greibach normal form.
- The example CFG's productions are listed, and the absence of unit and null productions is noted.
- The CFG is confirmed to be in Chomsky normal form, and non-terminal symbols are renamed according to the steps.
Chapter 4
The instructor emphasizes the need for non-terminals to be in ascending order in the productions.
- The productions of the example CFG are checked to ensure non-terminals are in ascending order (I < J).
- One production violating the rule (I >= J) is identified, signaling a need for further adjustment.
Chapter 5
A problematic production is addressed to align with Greibach normal form rules.
- The instructor demonstrates how to resolve the issue by replacing the problematic variable with the appropriate values.
- The process is repeated until the production adheres to the rule that non-terminals must be in ascending order.
Chapter 6
Left recursion in the example CFG is identified, with the resolution to be discussed in the next lecture.
- Left recursion is recognized in one of the productions where a non-terminal points to itself at the beginning of a production.
- The instructor notes that steps to remove left recursion will be covered in a subsequent lecture.
Chapter 7
The video concludes with a summary of the conversion process and a preview of the following lecture on removing left recursion.
- The steps covered in the lecture summarize the process to convert a CFG to Greibach normal form up to the point of resolving left recursion.
- The upcoming lecture will detail the process for removing left recursion to complete the conversion.
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