GATE CSE 2007 | Finite Automata and Regular Language Question 61 | Theory of Computation

GATE CSE 2007

MCQ (Single Correct Answer)

-0.6

A minimum state deterministic finite automation accepting the language $$L = \left\{ {w\left| {w \in } \right.\,\,{{\left\{ {0,1} \right\}}^ * },\,\,} \right.$$ number of $$0'$$s and $$1'$$s in $$w$$ are divisible by $$3$$ and $$5$$, respectively$$\left. \, \right\}$$ has

$$15$$ states

$$11$$ states

$$10$$ states

$$9$$ states

GATE CSE 2006

MCQ (Single Correct Answer)

-0.6

If $$s$$ is a string over $${\left( {0 + 1} \right)^ * }$$ then let $${n_0}\left( s \right)$$ denote the number of $$0'$$ s in $$s$$ and $${n_1}\left( s \right)$$ the number of $$1'$$s in $$s.$$ Which one of the following languages is not regular?

$$L = \left\{ {s \in {{\left( {0 + 1} \right)}^ * }\left| {{n_0}\left( s \right)\,\,} \right.} \right.$$ is a $$3$$-digit prime$$\left. \, \right\}$$

$$L = \left\{ {s \in {{\left( {0 + 1} \right)}^ * }\left| {\,\,} \right.} \right.$$ for every prefix $$s'$$ of $$s.$$ $$\,\left| {{n_0}\left( {{s^,}} \right) - {n_1}\left( {{s^,}} \right)\left| { \le \left. 2 \right\}} \right.} \right.$$

$$L = \left\{ {s \in {{\left( {0 + 1} \right)}^*}\left\| {{n_0}\left( s \right) - {n_1}\left( s \right)\left| { \le \left. 4 \right\}} \right.} \right.} \right.$$

$$L = \left\{ {s \in {{\left( {0 + 1} \right)}^ * }} \right.\left| {{n_0}\left( s \right)} \right.$$ mod $$7 = {n_1}\left( s \right)$$ mod $$5 = \left. 0 \right\}$$

GATE CSE 2006

MCQ (Single Correct Answer)

-0.6

Consider the regular language $$L = {\left( {111 + 11111} \right)^ * }.$$ The minimum number of states in any $$DFA$$ accepting this language is

$$3$$

$$5$$

$$8$$

$$9$$

GATE CSE 2005

MCQ (Single Correct Answer)

-0.6

Consider the machine $$M:$$ The language recognized by $$M$$ is: GATE CSE 2005 Theory of Computation - Finite Automata and Regular Language Question 40 English

GATE CSE 2005 Theory of Computation - Finite Automata and Regular Language Question 40 English

$$\left\{ {w\,\, \in \,\left\{ {a,b} \right\}{}^ * \left| \, \right.} \right.$$ every $$a$$ in $$w$$ is followed by exactly two $$\left. {b's} \right\}$$

$$\left\{ {w\,\, \in \,\left\{ {a,b} \right\}{}^ * \left| \, \right.} \right.$$ every $$a$$ in $$w$$ is followed by at least two $$\left. {b's} \right\}$$

$$\left\{ {w\,\, \in \,\left\{ {a,b} \right\}{}^ * \left| \, \right.} \right.$$ $$w$$ contains the substring $$\,\left. {'abb'\,\,} \right\}\,$$

$$\left\{ {w\,\, \in \,\left\{ {a,b} \right\}{}^ * \left| \, \right.} \right.$$ $$w$$ does not contain $$'aa'$$ as a substring$$\left. \, \right\}$$

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