CSCI 301 L19 Worksheet

Lecture 19 - Exercises

Part A - DFA Design

Draw a diagram for a DFA that accepts each of the following languages over the alphabet \(\{a, b\}\).

1. \(L = \{a\}\)
2. \(L = \varnothing\)
3. \(L = \{\epsilon\}\)
4. \(L = \{ab, abab, ababab, \ldots\}\)

Draw a diagram for a DFA for each of the following languages over \(\Sigma = \{0, 1\}\):

4. \(L = \{w : |w| \text{ is even}\}\)
5. \(L = \{w : w \text{ ends with a $1$}\}\)

Part B - Regular Operations

Consider the alphabet \(\Sigma = \{a, b\}\), and define the four “base case” regular languages as follows:

• \(N = \varnothing\)
• \(E = \{\epsilon\}\)
• \(A = \{a\}\)
• \(B = \{b\}\)

For each of the following, apply the given regular operations(s) and write the result using roster notation:

1. \(A \cup B\)
2. \(BA\)
3. \(AN\)
4. \(AEB\)
5. \(A^*\)
6. \((AB)^*\)
7. \(E^*\)

For each of the following languages, write how to construct it from the base case languages over \(\Sigma\) using only regular operations.

1. \(\{\epsilon, a, ab, abb, abbb, \ldots\}\)
2. \(\{aa, aba, abba, \ldots\}\)