1

GATE CSE 2014 Set 2

MCQ (Single Correct Answer)

+2

-0.6

Let $${L_1} = \left\{ {w \in \left\{ {0,1} \right\}{}^ * \left| w \right.} \right.$$ has at least as many occurrences of $$(110)'s$$ as $$(011)'s$$$$\left. \, \right\}$$. Let $${L_2} = \left\{ {w \in \left\{ {0,\,\,1} \right\}{}^ * \left| w \right.} \right.$$ has at least as many occurrences of $$(000)'s$$ as $$(111)'s$$$$\left. \, \right\}$$. Which one of the following is TRUE?

2

GATE CSE 2013

MCQ (Single Correct Answer)

+2

-0.6

Consider the following languages

$${L_1} = \left\{ {{0^p}{1^q}{0^r}\left| {p,q,r \ge 0} \right.} \right\}$$

$${L_2} = \left\{ {{0^p}{1^q}{0^r}\left| {p,q,r \ge 0,p \ne r} \right.} \right\}$$

$${L_1} = \left\{ {{0^p}{1^q}{0^r}\left| {p,q,r \ge 0} \right.} \right\}$$

$${L_2} = \left\{ {{0^p}{1^q}{0^r}\left| {p,q,r \ge 0,p \ne r} \right.} \right\}$$

Which one of the following statements is **FALSE?**

3

GATE CSE 2012

MCQ (Single Correct Answer)

+2

-0.6

Consider the set of strings on $$\left\{ {0,1} \right\}$$ in which, every substring of $$3$$ symbols has at most two zeros. For example, $$001110$$ and $$011001$$ are in the language, but $$100010$$ is not. All strings of length less than $$3$$ are also in the language. A partially completed $$DFA$$ that accepts this language is shown below.

The missing arcs in the $$DFA$$ are

4

GATE CSE 2011

MCQ (Single Correct Answer)

+2

-0.6

Definition of the language $$L$$ with alphabet $$\left\{ a \right\}$$ is given as following. $$L = \left\{ {{a^{nk}}} \right.\left| {k > 0,\,n} \right.$$ is a positive integer constant$$\left. \, \right\}$$

What is the minimum number of states needed in a $$DFA$$ to recognize $$L$$?

Questions Asked from Finite Automata and Regular Language (Marks 2)

Number in Brackets after Paper Indicates No. of Questions

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