CSE331: Automata & Computability Assignment 2 Total Marks – 20 1. [4×5 = 20 points) Construct DFAs for the following languages. Give both the state diagrams and the state-transition tables. a. The set of binary strings that start with “11” and end with “01”. E = {0,1,2} b. The set of binary strings which, when converted into an integer number, are divisible by 6. The string must not have leading zeros (for example, 110, 0, and 11110 will be accepted, 0110, 1111, and 101 will be rejected). Empty string (€) will be rejected. (E = {0,1} C. The set of binary strings whose length is odd and has 1 in every even position. (The strings 0 and 1 will also be accepted by the DFA). E={0,1}. For example: 010, 01111, 11010, 1111010, etc. d. The set of binary strings that do not contain exactly two O’s. (it may have more than 20’s, or less). Empty string (€) will be accepted. = {0,1} e. The set of binary strings with even numbers of O’s and with 1’s in pairs. I = {0,1}. For example: €, 11, 00, 1111, 0110, 110110, 01100110. G grammarly for Chrome Х Welcome to the Grammarly beta for Google Docs! Sign up to turn on Grammarly suggestions in your Google Docs Sign up Already have an account? Log in

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  1. The set of binary strings that start with “11” and end with “01”. Σ = {0,1,2}
  2. The set of binary strings which, when converted into an integer number, are divisible by 6. The string must not have leading zeros (for example, 110, 0, and 11110 will be accepted, 0110, 1111, and 101 will be rejected). Empty string (ϵ) will be rejected. (Σ = {0,1}
  3. The set of binary strings whose length is odd and has 1 in every even position. (The strings 0 and 1 will also be accepted by the DFA). Σ={0,1}. For example: 010, 01111, 11010, 1111010, etc.
  4. The set of binary strings that do not contain exactly two 0’s. (it may have more than 2 0’s, or less). Empty string (ϵ) will be accepted. Σ = {0,1}
  5. The set of binary strings with even numbers of 0’s and with 1’s in pairs. Σ = {0,1}. For example: ϵ, 11, 00, 1111, 0110, 110110, 01100110.

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