MC 306 Theory of Computation Thursday, 103003

1
MC 306 Theory of ComputationThursday, 10/30/03

• Last time
• Began discussing PDAs
• Todays Class
• Exam 2 Information
• Optional HW 4 due Tuesday, 11/4/03 at class
  time
• More on PDAs
• More examples
• Equivalence of PDAs and CFGs

• Reading Still 3.4
• Exercises No new exercises

2
Exam 2 Information

• TAKE-HOME EXAM
• Distributed at end of class on Thursday 11/6
• Due at my office by 5 PM sharp on Monday 11/10
• NO LATE EXAMS ACCEPTED
• STRICT HONOR CODE RULES IN FORCE
• You may consult any class notes, handouts, or our
  text
• You may use JFLAP (except if instructed
  otherwise)
• YOU MAY NOT USE ANY OTHER REFERENCES
• YOU MAY NOT SPEAK ABOUT THE PROBLEMS WITH ANYONE
  BUT ME.

3
Exam 2 Topics

• Exam 2 covers all topics beginning after Exam
  1, and ending with material covered in todays
  class
• Note Be sure to review slides and class notes in
  conjunction with text, since we sometimes
  deviated from text coverage
• Chapter 2 Finite automata and regular languages
• Sections 2.4-2.5
• Equivalence of regular expressions and NFAs
  non-regular languages Pumping Lemma proving
  languages are non-regular (using PL and closure
  properties)
• Chapter 3 Context-free languages
• Sections 3.1-3.4, 3.7
• Context-free grammars parse trees leftmost
  derivations equivalence of derivations
  ambiguity Chomsky Normal Form PDAs equivalence
  of PDAs and CFGs

4
Equivalence of PDAs and CFGs

• We have already seen how to convert a CFG to an
  equivalent PDA
• There is also an algorithm to convert a PDA to an
  equivalent CFG (see text). Thus
• Theorem A language L is context-free IFF it is
  accepted by some CFG GL IFF it is accepted by
  some PDA ML
• Theorem Every regular language is context-free.