Module #2b: Properties of Context-Free Languages

Objectives

1. Create equivalent CFG's:
   • with a nonrecursive start
     
   • without (most) lambda (epsilon) productions
     
   • without useless symbols
     
   • without unit (aka singleton) productions (aka chain rules)
     
2. Convert a grammar to Chomsky Normal Form
   
3. Define and occasionally convert grammars to Greibach Normal Form
   
4. Define closure properties for CFL's
   
5. Define decision properties for CFL's
   

Topics

1. Elimination of epsilon productions
   
2. Elimination of unit rules
   
3. Elimination of useless symbols
   
4. Chomsky Normal Form
   
5. Greibach Normal Form
   
6. Closure Properties of CFL's
   

Background Material

0. Text

Sudkamp: Chapter 4

1. Wikepedia: Context-Free Grammars
2. Grahne Text Slides: Pages 225-end
3. Busch, Shiri & Grahne: [PDF] Simplification of CFG's
4. Busch, Shiri & Grahne: [PDF] Closure Properties
5. Video of Grammatical Transformations
6. Video of Chomsky Normal Form
7. Matthew Reiter's Excellent Grammar convertors

Old Homeworks

Homework Fall 2005 [PDF]
Homework Solutions Fall 2005 [PDF]

Homework Summer 2006 [PDF]
Homework Solutions Summer 2006 [DOC] [PDF]