Summary of "Non-Deterministic CFGs"

Summary of “Non-Deterministic CFGs” Video

Main Ideas and Concepts

Classification of Context-Free Grammars (CFGs): CFGs can be classified into three main categories:
- Ambiguous vs. Unambiguous CFGs
- Left Recursive vs. Right Recursive CFGs
- Non-deterministic vs. Deterministic CFGs
Ambiguity and Recursion in CFGs:
- Ambiguous CFGs cause issues such as violation of associativity and precedence.
- Left recursive CFGs are problematic for top-down parsers, which prefer right recursive CFGs.
- Techniques exist to convert ambiguous CFGs to unambiguous ones and left recursive CFGs to right recursive CFGs.
Non-Deterministic vs. Deterministic CFGs:
- Non-deterministic CFGs have multiple productions with a common prefix, for example: [ A \rightarrow \alpha \beta_1 \mid \alpha \beta_2 \mid \alpha \beta_3 ]
- From a state machine perspective, from state ( A ), the machine can move to any of the states ( \beta_1, \beta_2, \beta_3 ) after reading the common prefix ( \alpha ).
- Top-down parsers, when faced with such grammars, must backtrack because they cannot decide which production to choose after seeing only the common prefix.
- Backtracking occurs because the parser chooses production rules based only on the prefix ( \alpha ), without full lookahead.
Problem of Common Prefix (Non-Determinism):
- The main source of non-determinism is the presence of common prefixes in multiple productions.
- This causes inefficiency due to repeated backtracking in top-down parsing.
Left Factoring Procedure:
- Left factoring is a method to eliminate non-determinism by factoring out the common prefix.
- The grammar is rewritten as: [ A \rightarrow \alpha A’ ] [ A’ \rightarrow \beta_1 \mid \beta_2 \mid \beta_3 ]
- This transformation creates a deterministic CFG suitable for top-down parsing.
- Left factoring reduces backtracking by allowing the parser to make decisions after reading the common prefix once.
Summary of Session:
- Reviewed CFG classifications.
- Explained non-determinism and its relation to common prefixes.
- Introduced left factoring as a technique to convert non-deterministic CFGs into deterministic ones.
- Mentioned future sessions will cover solved problems on eliminating non-determinism.

Detailed Methodology: Left Factoring Procedure

Given a non-deterministic CFG with productions having common prefixes, for example: [ A \rightarrow \alpha \beta_1 \mid \alpha \beta_2 \mid \alpha \beta_3 ]

Steps to Left Factor:

Identify the longest common prefix ( \alpha ) among the productions.
Replace the original productions with a single production that generates the common prefix followed by a new non-terminal: [ A \rightarrow \alpha A’ ]
Define the new non-terminal ( A’ ) to generate the alternatives that follow the common prefix: [ A’ \rightarrow \beta_1 \mid \beta_2 \mid \beta_3 ]
This eliminates the need for backtracking since the parser can now deterministically choose the correct production after reading ( \alpha ).

Speakers/Sources Featured

Primary Speaker: The session presenter/lecturer (unnamed) who explains the concepts and methodology related to non-deterministic CFGs and left factoring.

This summary captures the core instructional content and methodology from the video on non-deterministic context-free grammars and how to convert them to deterministic CFGs using left factoring.