1

GATE CSE 2011

MCQ (Single Correct Answer)

+2

-0.6

A deterministic finite automation $$(DFA)$$ $$D$$ with alphabet $$\sum { = \left\{ {a,b} \right\}} $$ is given below

Which of the following finite state machines is a valid minimal $$DFA$$ which accepts the same languages as $$D?$$

2

GATE CSE 2010

MCQ (Single Correct Answer)

+2

-0.6

Consider the languages
$$$\eqalign{
& {L_1} = \left\{ {{0^i}{1^j}\,\left| {i \ne j} \right.} \right\},\,{L_2} = \left\{ {{0^i}{1^j}\,\left| {i = j} \right.} \right\}, \cr
& {L_3} = \left\{ {{0^i}{1^j}\,\left| {i = 2j + 1} \right.} \right\}, \cr
& {L_4} = \left\{ {{0^i}{1^j}\,\left| {i \ne 2j} \right.} \right\}, \cr} $$$

3

GATE CSE 2008

MCQ (Single Correct Answer)

+2

-0.6

Which of the following statement is false?

4

GATE CSE 2008

MCQ (Single Correct Answer)

+2

-0.6

Which of the following statements are true?

$$1.$$ Every left-recursive grammar can be converted to a right-recursive grammar and vice-versa

$$2.$$ All ε-productions can be removed from any context-free grammar by suitable transformations

$$3.$$ The language generated by a context-free grammar all of whose productions are of the form $$X \to w$$ or $$X \to wY$$ (where, $$w$$ is a string of terminals and $$Y$$ is a non terminal), is always regular

$$4.$$ The derivation trees of strings generated by a context-free grammar in Chomsky Normal Form are always binary trees

$$1.$$ Every left-recursive grammar can be converted to a right-recursive grammar and vice-versa

$$2.$$ All ε-productions can be removed from any context-free grammar by suitable transformations

$$3.$$ The language generated by a context-free grammar all of whose productions are of the form $$X \to w$$ or $$X \to wY$$ (where, $$w$$ is a string of terminals and $$Y$$ is a non terminal), is always regular

$$4.$$ The derivation trees of strings generated by a context-free grammar in Chomsky Normal Form are always binary trees

Questions Asked from Push Down Automata and Context Free Language (Marks 2)

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Discrete Mathematics

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