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Theory of Computation
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  • Gate
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Topics include regular and context-free languages, decidable and undecidable problems, reducibility, recursive function theory, time and space measures on computation, completeness, hierarchy theorems, inherently complex problems, oracles, probabilistic computation, and interactive proof systems.

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Document information

  • April 3, 2023
  • 5
  • 2022/2023
  • Class notes
  • Mrs.prachi
  • B.e 1st year to final year

Subjects

  • inforamation technology
  • toc

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  • Gate
All documents for this subject (193)

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“Sentential Forms”.

1. State true or false:
Statement: Every right-linear grammar generates a regular language.
a) True
b) False
View Answer

Answer: a


Explanation: A CFG is said to right linear if each production body has at most one
variable, and that variable is at the right end. That is, all productions of a right linear
grammar are of the form A->wB or A->w, where A and B are variables while w is some
terminal.


2. What the does the given CFG defines?
S->aSbS|bSaS|e and w denotes terminal
a) wwr
b) wSw
c) Equal number of a’s and b’s
d) None of the mentioned
View Answer

Answer: c


Explanation: Using the derivation approach, we can conclude that the given grammar
produces a language with a set of string which have equal number of a’s and b’s.


3. If L1 and L2 are context free languages, which of the following is context free?
a) L1*
b) L2UL1
c) L1.L2
d) All of the mentioned
View Answer

Answer: d

, Explanation: The following is a theorem which states the closure property of context free
languages which includes Kleene operation, Union operation and Dot operation.


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4. For the given Regular expression, the minimum number of variables including starting
variable required to derive its grammar is:
(011+1)*(01)*
a) 4
b) 3
c) 5
d) 6
View Answer

Answer: c


Explanation: The grammar can be written as:


S->BC


B->AB|ε


A->011|1


C->DC|ε


D->01


5. For the given Regular expression, the minimum number of terminals required to derive its
grammar is:
(011+1)*(01)*
a) 4
b) 3
c) 5
d) 6
View Answer

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