GATE CSE 2001 | Finite Automata and Regular Language Question 74 | Theory of Computation

GATE CSE 2001

MCQ (Single Correct Answer)

-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?

$$8$$

$$14$$

$$15$$

$$48$$

GATE CSE 2000

MCQ (Single Correct Answer)

-0.6

What can be said about a regular language $$L$$ over $$\left\{ a \right\}$$ whose minimal finite state automation has two states?

Must be $$\left\{ {{a^n}\left| n \right.\,\,} \right.$$ is odd $$\left. \, \right\}$$

Must be $$\left\{ {{a^n}\left| n \right.\,\,} \right.$$ is even $$\left. \, \right\}$$

Must be $$\left\{ {{a^n}\left| {n \ge } \right.\,\,} \right.0\left. \, \right\}$$

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$$\left. \, \right\}$$

GATE CSE 1998

MCQ (Single Correct Answer)

-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

$$2$$

$$5$$

$$8$$

$$3$$

GATE CSE 1997

MCQ (Single Correct Answer)

-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?

$${0^ * }{\left( {1 + 0} \right)^ * }$$

$${0^ * }\,\,{1010^ * }$$

$${0^ * }\,\,{1^ * }\,\,{01^ * }$$

$${0^ * }{\left( {10 + 1} \right)^ * }$$

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