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how many number of states do we require for evaluating a string which has odd count of 0's odd count of 1's even count of 2'sa.14b.16c.4d.8

Question

How many states do we require for evaluating a string which has:

  • odd count of 0s
  • odd count of 1s
  • even count of 2s?

Options:

  • a. 14
  • b. 16
  • c. 4
  • d. 8
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Solution

To evaluate a string which has an odd count of 0's, an odd count of 1's, and an even count of 2's, we need to consider all possible combinations of these conditions.

Step 1: For the odd count of 0's, we need 2 states: one for when the count is even (initial state), and one for when the count is odd.

Step 2: Similarly, for the odd count of 1's, we also need 2 states: one for when the count is even (initial state), and one for when the count is odd.

Step 3: For the even count of 2's, we only need 2 states: one for when the count is even (initial state), and one for when the count is odd.

Step 4: Since these conditions can occur in any combination, we need to consider all possible combinations of these states. This gives us a total of 2 (for 0's) * 2 (for 1's) * 2 (for 2's) = 8 states.

So, the correct answer is (d) 8.

This problem has been solved

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