CSci 4011: Formal Languages and Automata Theory
Fall 2008, University of Minnesota
Homework 2

Posted: Sept 16, 2008
Due: Sept 30, 2008

Reminder: Assignments are due in class before the start of class on the day indicated.

Problem 1

Do Exercise 1.28 parts a and c from the book.

Problem 2

Do Problem 1.21 part b from the book.

Problem 3

Do Problem 1.41 from the book.

Problem 4

Do Problem 1.46 parts a and c from the book.

Problem 5

Do Problem 1.47 from the book.

Hint: You may find it useful to use the fact that regular languages are closed under complementation.

Problem 6

Do Problem 1.49 from the book.

Problem 7

If C is any set of languages, then we define ∪ C as follows:

∪ C = { s | s ∈ L for some L ∈ C }

Now, if C is a set of regular languages, is ∪ C also regular? If you claim that it is, you must prove this. If you claim it is not, then you must provide a counterexample.

Hint: If C is a finite set, then we already know the answer: regular languages are closed under finite union by a theorem we proved in class. Thus, you have to think of the case when C is an infinite set to answer this question.

Last updated on Sept 18, 2008 by gopalan@cs.umn.edu

CSci 4011: Formal Languages and Automata Theory Fall 2008, University of Minnesota Homework 2