AlgoMaster

Engineering Solutions

Context-Free Grammar Parser

Design and test context-free grammars for parsing structured languages and expressions

Context-Free Grammar (CFG)

Context-Free Grammars are formal grammar systems that define the syntax of context-free languages. They are essential for parsing programming languages, XML, and mathematical expressions.

Theory & Concepts

Definition:

A Context-Free Grammar is a 4-tuple G = (V, Σ, R, S) where V is a finite set of non-terminals, Σ is a finite set of terminals, R is a finite set of production rules, and S is the start symbol.

Key Points:

  • Production rules define how non-terminals expand into terminals and non-terminals
  • Supports nested structures and recursive definitions
  • Foundation for compiler design and parser construction
  • Used in programming language syntax specification

Applications:

  • Programming language parsers and compilers
  • XML and markup language processing
  • Mathematical expression evaluation
  • Natural language processing systems

University Guidelines

Exam Weightage
8-10 marks Marks

Syllabus Coverage:

  • Context-Free Grammar definition and components
  • Derivations: leftmost and rightmost
  • Parse trees and ambiguity
  • Chomsky Normal Form and Greibach Normal Form
  • Pumping Lemma for Context-Free Languages

Common Questions:

  • Design CFG for given language specifications
  • Convert CFG to CNF or GNF
  • Check if a string belongs to a given CFG
  • Eliminate left recursion and left factoring

Exam Tips:

Focus on leftmost and rightmost derivations
Practice converting between different normal forms
Remember the pumping lemma for context-free languages
Understand the relationship between CFGs and pushdown automata

Algorithm Details

O(n³) for CYK parsing
Time Complexity
O(n²) for parse table
Space Complexity

Algorithm Steps:

  1. 1Define terminals, non-terminals, and start symbol
  2. 2Create production rules for the language
  3. 3Apply productions to derive target string
  4. 4Verify derivation and parse tree construction

Example Grammars

Terminals

id
+
*
(
)

Non-terminals

E
T
F

Productions

→
→
→
→
→
→

Target String

Grammar Visualization

Terminals:
id+*()
Non-terminals:
ETF
Production Rules:
E→T + E
E→T
T→F * T
T→F
F→( E )
F→id