1
GATE CSE 2003
MCQ (Single Correct Answer)
+2
-0.6
Consider the following deterministic finite state automation $$M.$$

Let $$S$$ denote the set of seven bit binary strings in which the first, the fourth, and the last bits are $$1$$. The number of strings in $$S$$ that are accepted by $$M$$ is

A
$$1$$
B
$$5$$
C
$$7$$
D
$$8$$
2
GATE CSE 2002
MCQ (Single Correct Answer)
+2
-0.6
The smallest finite automaton which accepts the language
$$L = \left. {\left\{ x \right.} \right|$$ length of $$x$$ is divisible by $$\left. 3 \right\}$$ has
A
$$2$$ states
B
$$3$$ states
C
$$4$$ states
D
$$5$$ states
3
GATE CSE 2002
MCQ (Single Correct Answer)
+2
-0.6
The Finite state machine described by the following state diagram with $$A$$ as starting state, where an arc label is $$x/y$$ and $$x$$ stands for $$1-bit$$ input and $$y$$ stands for $$2$$-bit output
A
Outputs the sum of the present and the previous bits of the input.
B
Outputs $$01$$ whenever the input sequence contains $$11$$
C
Outputs $$00$$ whenever the input sequence contains $$10$$
D
None of the above
4
GATE CSE 2001
MCQ (Single Correct Answer)
+2
-0.6
Consider a $$DFA$$ over $$\sum { = \left\{ {a,\,\,b} \right\}}$$ 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?
A
$$8$$
B
$$14$$
C
$$15$$
D
$$48$$
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