Theory of Computation


Q191.

Consider the alphabet \Sigma={0, 1}, the null/empty string \lambda and the sets of strings X_{0}, X_{1}, \; and \; X_{2} generated by the corresponding non-terminals of a regular grammar. X_{0}, X_{1}, \; and \; X_{2} are related as follows. X_{0}=1X_{1} X_{1},=0X_{1}+1 X_{2} X_{2}=0X_{1}+ \{\lambda\} Which one of the following choices precisely represents the strings in X_{0}?
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Q192.

Choose the correct alternatives (More than one may be correct).Let R_{1} and R_{1} be regular sets defined over the alphabet \Sigma Then:
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Q193.

For S \in (0+1)^{*}, let d(s) denote the decimal value of s (e.g. d(101)=5). Let L={s \in (0+1)*| d(s) mod 5=2 and d(s) mod 7\neq4} Which one of the following statements is true?
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Q194.

Consider the regular expression R = (a + b)^* (aa + bb) (a + b)^* Which deterministic finite automaton accepts the language represented by the regular expression R?
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Q195.

Which of the following regular expressions represent(s) the set of all binary numbers that are divisible by three? Assume that the string \epsilon is divisible by three.[MSQ]
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Q196.

Which one of the following regular expressions represents the set of all binary strings with an odd number of 1's?
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Q197.

Which one of the following regular expressions represents the language: the set of all binary strings having two consecutive 0s and two consecutive 1s?
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Q198.

Consider the following definition of a lexical token id for an identifier in a programming language, using extended regular expressions: letter \rightarrow [A-Za-z] digit \rightarrow [0-9] id \rightarrow letter (letter\;| \;digit)^* Which one of the following Non-deterministic Finite-state Automata with - transitions accepts the set of valid identifiers? (A double-circle denotes a final state)
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Q199.

Which of the following regular expressions describes the language over\{0, 1\} consisting of strings that contain exactly two 1's?
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Q200.

Which of the following languages is regular?
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