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1. Number of states of FSM required to simulate behaviour of a computer with a memory capable of storing “m” words, each of length ‘n’.
Choose the correct option:
  • a) m x 2n

  • b) 2mn

  • c) 2(m+n)

  • d) all of the mentioned

For every Data here length is n and memory’s state is defined in terms of power of 2, Here the total memory capability for all the words = mn Hence the number of states is2<sup>mn</sup>.

2. An FSM with __________
Choose the correct option:
  • a) M can be transformed to Numeral relabeling its states

  • b) M can be transformed to N, merely relabeling its edges

  • c) Both of the mentioned

  • d) None of the mentioned

The Definition of FSM states that M can be transformed to N by relabeling its states or its edges.

3. Which of the following statement is correct?
Choose the correct option:
  • a) A Context free language can be accepted by a deterministic PDA

  • b) union of 2 CFLs is context free

  • c) The intersection of two CFLs is context free

  • d) The complement of CFLs is context free

Context-free languages are closed under the following operations. The Kleene star, the concatenation, the union and the intersection.

Which of the following is true?
Choose the correct option:
  • a) Only S1 is correct

  • b) Only S2 is correct

  • c) Both S1 and S2 are correct

  • d) None of S1 and S2 is correct

S1 can be written as (00)<sup>n</sup> where n &gt;= 1. And S2 can be written as (00)<sup> (m+n)</sup> where m &gt;=2 and n &gt;= 1. S2 can be further reduced to (00)<sup>x</sup> where x &gt;= 3. SO we can write regular grammars for both

5. Which of the following pairs of regular expressions are equivalent?
Choose the correct option:
  • a) 1(01)* and (10)*1

  • b) x (xx)* and (xx)*x

  • c) x+ and x+ x(*+)

  • d) All of the mentioned

Rule (pq)*p=p (qp)*

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