1
GATE CSE 2003
MCQ (Single Correct Answer)
+1
-0.3
The regular expression $${0^ * }\left( {{{10}^ * }} \right){}^ * $$denotes the same set as
A
$$\left( {{1^ * }0} \right){}^ * {1^ * }$$
B
$$0 + \left( {0 + 10} \right){}^ * $$
C
$$\left( {0 + 1} \right){}^ * 10\left( {0 + 1} \right){}^ * $$
D
None of the above.
2
GATE CSE 2003
MCQ (Single Correct Answer)
+1
-0.3
Consider the set $$\sum {^ * } $$ of all strings over the alphabet $$\,\sum { = \,\,\,\left\{ {0,\,\,\,1} \right\}.\sum {^ * } } $$ with the concatenation operator for strings
A
Does not from a group
B
Forms a non-commutative group
C
Does not have a right identity element
D
Forms a group if the empty string is removed from $${\sum {^ * } }$$
3
GATE CSE 2003
MCQ (Single Correct Answer)
+2
-0.6
Consider the $$NFA$$ $$M$$ shown below. GATE CSE 2003 Theory of Computation - Finite Automata and Regular Language Question 30 English

Let the language accepted by $$M$$ be $$L.$$ Let $${L_1}$$ be the language accepted by the $$NFA$$, $${M_1}$$ obtained by changing the accepting state of $$M$$ to a non accepting state and by changing the non accepting state of $$M$$ to accepting states. Which of the following statements is true?

A
$${L_1} = \left\{ {0,\,1} \right\}{}^ * - L$$
B
$${L_1} = \left\{ {0,\,1} \right\}{}^ * $$
C
$${L_1} \subseteq \,L$$
D
$${L_1} = \,L$$
4
GATE CSE 2003
MCQ (Single Correct Answer)
+2
-0.6
Consider the following deterministic finite state automation $$M.$$ GATE CSE 2003 Theory of Computation - Finite Automata and Regular Language Question 29 English

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
$$8$$
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