CS4311: Introduction to Computation Theory hw6

CS 4311 Introduction to Computation Theory
Homework 6: Chapter 2

Due: Wednesday, 10/18/06, beginning of class (Assigned: Wednesday, 10/11/06)

You are required to turn in answers to all the questions. However, only a random subset of the questions will be graded. While discussion with others is permitted and encouraged, the final work should be done individually. You are not allowed to work in groups. The answers, comments, and programs (if any) must be the original work of the author. You are allowed to build on material supplied in the class. If you use any other source than the current class notes and the textbook, specify it clearly.

1. In Chapter 1, we worked on a procedure to convert a regular expression to a DFA. This time, we would like to convert a regular expression to a CFG. Sketch a procedure to construct a CFG that generates the same language as a regular expression R. Make sure that you include all three base cases, and the cases for union, concatenation, and star as in Definition 1.52 of regular expressions.

2. (Problem 2.14) Convert the following CFG into an equivalent CFG in Chomsky normal form, using the procedure given in Theorem 2.9.

3. Construct a PDA that recognizes the languages below. Be sure to give a brief, English description of how your PDA works. In all parts the alphabet Σ is {0,1}.

4. (Exercise 2.12) Convert the CFG G4 given in Exercise 2.3 to an equivalent PDA using the procedure given in Theorem 2.20.