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Question

Consider the following DFA that generates set of strings over $\Sigma=\{a, b, c\}$

Now identify that which of the followings is the best description of the language for the above DFA

The correct answer is

$L = \{\text{Set of strings, all having even count (including 0) of substring 'abc'}\}$

The given question involves analyzing a DFA and determining the language it accepts over the alphabet \Sigma = \{a, b, c\}. To solve this, we'll examine the transitions in the DFA provided by the image.

DFA Diagram

In the DFA provided, the language can be identified by examining its states and transitions:

  1. The DFA starts at state q0, which is also the accepting state.
  2. State q0 transitions to itself upon encountering 'b' or 'c'.
  3. Entering state q1 occurs by reading 'a', transitioning eventually to the further states which form the pattern 'abc'.
  4. Upon reading 'abc', we return to an accepting state if continued transitions repeat this process.

By following these steps, the DFA essentially allows strings with blocks of 'abc' where:

  • The substring 'abc' can occur even number of times (0, 2, 4, etc.).
  • Any combination of 'a', 'b', and 'c' may appear before or after these even repetitions of 'abc', but they do not affect the acceptance as long as 'abc' appears an even number of times.

Considering this, the correct language from the options provided is:

L = \{\text{Set of strings, all having even count (including 0) of substring 'abc'}\}

This clearly matches the behavior and acceptance logic of the presented DFA where the transitions enable it to remove back to the initial state if 'abc' is completed in cycles.

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Important Questions from Finite Automata

  1. If NFA of 5 states excluding the initial state is converted into DFA, maximum possible number of states for the DFA is?

  2. A Language for which DFA exist is a________

  3. For a DFA accepting binary numbers whose decimal equivalent is divisible by 3, what are all the possible remainders?

  4. Minimum Number of states require to accept string ends with 101.

  5. Consider the DFA given below

    Which of the regular expressions given below represents the above DFA ?

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