Let L = (0+1)*1(0+1)⁽ⁿ⁻¹⁾ and following statements regrading language L:

1. The language L can be recognised by a non-deterministic automaton with (n+1) states.
2. Deterministic automaton recognises this language must have at least 2ⁿ states.

(Assume n≥1).
Which of the following statement(s) is/are correct?
(A) 1 only
(B) 2 only
(C) Both 1 and 2
(D) Neither 1 nor 2


Answer: (C)

Explanation: Both the statements are correct. This example shows that an exponential increase in the number of states in passing from a non-deterministic automaton to a corresponding determin- istic automaton is sometimes unavoidable.

Option (C) is True.


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