1
GATE CSE 2000
+2
-0.6
What can be said about a regular language $$L$$ over $$\left\{ a \right\}$$ whose minimal finite state automation has two states?
A
Must be $$\left\{ {{a^n}\left| n \right.\,\,} \right.$$ is odd $$\left. \, \right\}$$
B
Must be $$\left\{ {{a^n}\left| n \right.\,\,} \right.$$ is even $$\left. \, \right\}$$
C
Must be $$\left\{ {{a^n}\left| {n \ge } \right.\,\,} \right.0\left. \, \right\}$$
D
Either $$L$$ must be $$\left\{ {{a^n}\left| n \right.\,\,} \right.$$ is odd$$\left. \, \right\}\,\,$$ or $$L$$ must be $$\left\{ {{a^n}\left| n \right.} \right.$$ is even$$\left. \, \right\}$$
2
GATE CSE 1998
+2
-0.6
Let $$L$$ be the set of all binary strings whose last two symbols are the same. The number of states in the minimum state deterministic finite-state automaton accepting $$L$$ is
A
$$2$$
B
$$5$$
C
$$8$$
D
$$3$$
3
GATE CSE 1997
+2
-0.6
Which one of the following regular expressions over $$\left\{ {0,\,\,1} \right\}$$ denotes the set of all strings not containing $$100$$ as substring?
A
$${0^ * }{\left( {1 + 0} \right)^ * }$$
B
$${0^ * }\,\,{1010^ * }$$
C
$${0^ * }\,\,{1^ * }\,\,{01^ * }$$
D
$${0^ * }{\left( {10 + 1} \right)^ * }$$
4
GATE CSE 1995
+2
-0.6
A finite state machine with the following state table has a single input $$X$$ and a single out $$Z$$.

If the initial state is unknown, then the shortest input sequence to reach the final state $$C$$ is here, since initial make unknown $$m$$ $$10$$ input we can each final state $$C$$ with shortest path.

A
$$01$$
B
$$10$$
C
$$101$$
D
$$110$$
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