1
GATE CSE 2011
+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 $$D?$$

A
B
C
D
2
GATE CSE 2010
+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}\$
A
only $${L_2}$$ is context free
B
only $${L_2}$$ and $${L_3}$$ are context free
C
only $${L_1}$$ and $${L_2}$$ are context free
D
all are context free
3
GATE CSE 2008
+2
-0.6
Which of the following statement is false?
A
Every $$NFA$$ can be converted to an equivalent $$DFA$$
B
Every non-deterministic Turing machine can be converted to an equivalent deterministic Turing machine.
C
Every regular language is also a context- free language
D
Every subset of a recursively enumerable set is recursive
4
GATE CSE 2008
+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
A
$$1,2,3$$ and $$4$$
B
$$2, 3$$ and $$4$$ only
C
$$1,3$$ and $$4$$ only
D
$$1,2$$ and $$4$$ only
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