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 GATE CSE 2011 Theory of Computation - Finite Automata and Regular Language Question 38 English

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

A
GATE CSE 2011 Theory of Computation - Finite Automata and Regular Language Question 38 English Option 1
B
GATE CSE 2011 Theory of Computation - Finite Automata and Regular Language Question 38 English Option 2
C
GATE CSE 2011 Theory of Computation - Finite Automata and Regular Language Question 38 English Option 3
D
GATE CSE 2011 Theory of Computation - Finite Automata and Regular Language Question 38 English Option 4
2
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 $$L$$?

A
$$k+1$$
B
$$n+1$$
C
$${2^{n + 1}}$$
D
$${2^{k + 1}}$$
3
GATE CSE 2010
MCQ (Single Correct Answer)
+2
-0.6
Let $$L = \left\{ {w \in {{\left( {0 + 1} \right)}^ * }\left| {\,w} \right.} \right.$$ has even number of $$\,\left. {1's} \right\},$$ i.e $$L$$ is the set of all bit strings with even number of $$1's.$$ which one of rhe regular expression below represents $$L.$$
A
$$\left( {{0^ * }{{10}^ * }1} \right){}^ * $$
B
$${0^ * }\left( {{{10}^ * }{{10}^ * }} \right){}^ * $$
C
$${0^ * }\left( {{{10}^ * }1} \right){}^ * {0^ * }$$
D
$${0^ * }\,\,1\left( {{{10}^ * }1} \right){}^ * {10^ * }$$
4
GATE CSE 2010
MCQ (Single Correct Answer)
+2
-0.6
Let $$w$$ be any string of length $$n$$ in $${\left\{ {0,1} \right\}^ * }$$. Let $$L$$ be the set of all substrings of $$w.$$ What is the minimum number of states in a non-deterministic finite automation that accepts $$L$$?
A
$$n-1$$
B
$$n$$
C
$$n+1$$
D
$${2^{n + 1}}$$
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