CS4311: Introduction to Computation Theory hw6

CS 4311 Introduction to Computation Theory
Homework 7: Chapters 3 and 4

Due: Wednesday, 10/22/03, beginning of class (Assigned: Wednesday, 10/15/03)

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. (Problem 3.11) A Turing machine with doubly infinite tape is similar to an ordinary Turing machine except that the tape is infinite to the left as well as to the right. The tape is initially filled with blanks except for the portion that contains the input. Computation is defined as usual except that the head never encounters an end to the tape as it moves leftward. Show that this type of Turing machine recognizes the class of Turing-recognizable languages.

2. (Exercise 3.14 b,d,e) Show that the collection of decidable languages is closed under the operations of

3. (Exercise 3.15 b,c,d) Show that the collection of Turing-recognizable languages is closed under the operations of

4. (Exercise 4.1) Answer all parts for the following DFA M and give reasons for your answers.


a. Is < M,0100 > ∈ ADFA?
b. Is < M,011 > ∈ ADFA?
c. Is < M > ∈ ADFA?
d. Is < M,0100 > ∈ AREX?
e. Is < M > ∈ EDFA?
f. Is < M,M > ∈ EQDFA?