Q. A minimum state deterministic finite automaton accepting the language L={w | w ε {0,1} *, number of 0s and 1s in w are divisible by 3 and 5, respectively} has

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Q. Let L1 = {w ∈ {0,1}∗ | w has at least as many occurrences
of (110)’s as (011)’s}.

Let L2 = { ∈ {0,1}∗ | w has at least as many occurrences
of (000)’s as (111)’s}.

Which one of the following is TRUE?

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Q. The length of the shortest string NOT in the language (over Σ = {a, b}) of the following regular expression is ______________.

a*b*(ba)*a*

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Q. Consider the regular language L = (111 + 11111)*. The minimum number of states in any DFA accepting this languages is:

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Q. Let Nf and Np denote the classes of languages accepted by non-deterministic finite automata and non-deterministic push-down automata, respectively. Let Df and Dp denote the classes of languages accepted by deterministic finite automata and deterministic push-down automata, respectively. Which one of the following is TRUE?

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Q. The regular expression 0*(10*)* denotes the same set as

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Q. The smallest finite automation which accepts the language {x | length of x is divisible by 3} has :

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Q. Given an arbitary non-deterministic finite automaton (NFA) with N states, the maximum number of states in an equivalent minimized DFA is at least

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Q. Consider a DFA over ∑ = {a, b} accepting all strings which have number of a’s divisible by 6 and number of b’s divisible by 8. What is the minimum number of states that the DFA will have?

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Q. Let S and T be language over Σ = {a,b} represented by the regular expressions (a+b*)* and (a+b)*, respectively. Which of the following is true?

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Q. Let L denotes the language generated by the grammar S -> 0S0/00. Which of the following is true?

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Q. What can be said about a regular language L over {a} whose minimal finite state automaton has two states?

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Q. How many minimum states are required in a DFA to find whether a given binary string has odd number of 0's or not, there can be any number of 1's.

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Q. Consider alphabet ∑ = {0, 1}, the null/empty string λ and the sets of strings X0, X1 and X2 generated by the corresponding non-terminals of a regular grammar. X0, X1 and X2 are related as follows:

X0 = 1 X1
X1 = 0 X1 + 1 X2
X2 = 0 X1 + {λ}

Which one of the following choices precisely represents the strings in X0?

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Q. The number of states in the minimal deterministic finite automaton corresponding to the regular expression (0 + 1)*(10) is ____________

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Q. Let T be the language represented by the regular expression Σ∗0011Σ∗ where Σ = {0, 1}. What is the minimum number of states in a DFA that recognizes L' (complement of L)?

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Q. Which one of the following regular expressions is NOT equivalent to the regular expression (a + b + c) *?

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Q. Let L be a regular language and M be a context-free language, both over the alphabet Σ. Let Lc and Mc denote the complements of L and M respectively. Which of the following statements about the language Lc∪ Mc is TRUE?

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Q. Which of the following statements is TRUE about the regular expression 01*0?

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Q. The language {0^n 1^n 2^n | 1 ≤ n ≤ 10^6} is

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