CS4311: Introduction to Computation Theory hw3

CS 4311 Introduction to Computation Theory
Homework 3: Chapter 1

Due: Wednesday, 9/27/06, beginning of class (Assigned: Wednesday, 9/20/06)

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. (similar to Exercise 1.2) Give a formal description of the machines pictured below.

2. (Parts of Exercises 1.4-1.6) Give state diagrams for DFAs recognizing the languages below.

3. (Exercise 1.16b) Use the construction given in Theorem 1.39 to convert the following nondeterministic finite automaton to an equivalent deterministic finite automaton.

4. (Exercise 1.11) Prove that every NFA can be converted to an equivalent one that has a single accept state. Is the reverse true? In other words, can every NFA with a single accept state be converted to one that has more than one accept state?

5. Use the construction given in the proof of Theorem 1.45 to give the state diagram of an NFA recognizing the union of the two languages recognized by the DFAs in problem 1.

6. Use the construction given in the proof of Theorem 1.47 to give the state diagram of an NFA recognizing the concatenation of the two languages recognized by the DFAs in problem 1.

7. Use the construction given in the proof of Theorem 1.49 to give the state diagram of an NFA recognizing the star of the language recognized by DFA M1 in problem 1.