CSCI 301 L22 Worksheet

Lecture 22 - Exercises

Part A - The Language Accepted by a FA

Consider again the following DFA over alphabet \(\Sigma = \{0,1\}\):

Which of the following strings are accepted by this machine?

  1. \(1\)

  2. \(00\)

  3. \(001\)

  4. \(10101\)

  5. \(100\)

  6. \(1000\)

  7. Describe (informally, in English) the language accepted by this machine.

Part D - DFA Design

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

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

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

  1. \(L = \{w : |w| \text{ is divisible by 3}\}\)
  2. \(L = \{w : w \text{ as a binary number is divisible by 4}\}\)