In the name of ALLAH, the most beneficient, the most merciful

Theory of Computation (CS701)

Subjective, Short Questions from Past Papers

 

Subjective Questions

Question

(Mid Term, Marks = 10, Lesson No. )

CONNECTED = {| is a connected undirected graph}. Give an algorithm that decides this language and show that CONNECTED € P.

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Question

(Mid Term, Marks = 5, Lesson No. )

In numbers 561, 2984. Show that these numbers relatively prime or not.

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Question

(Mid Term, Marks = 5, Lesson No. )

Is the following statement TRUE or FALSE? Justify your answer. ∀x∀y∃z [ R1(x, y, z) ∨ R1(y, x, z) ∨ R2(x, y) ], where universe is the set of positive integers and R1 = MINUS, that is, MINUS (x, y, z) = TRUE whenever x – y = z, and R2(x, y) = TRUE whenever x = y.

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Question

(Mid Term, Marks = 5, Lesson No. )

Show that the set of all positive real numbers has one-to-one correspondence with the set of all real numbers.

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Question

(Mid Term, Marks = 5, Lesson No. )

Consider the pair of numbers 64 and 32965. Show that they are relatively prime or not.

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Question

(Mid Term, Marks = 10, Lesson No. )

In the Silly Post Correspondence Problem (SPCP), the iop string in each pairhas the same length as the bottom string. Show that SPCP is decidable.

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Question

(Mid Term, Marks = 10, Lesson No. )

Show that some true statements in TH(N, +, x) are not provable.

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Question

(Mid Term, Marks = 5, Lesson No. )

Show that the set of all odd integers has one-to-one correspondence with the set of all even integers.

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Question

(Mid Term, Marks = 5, Lesson No. )

Consider the pair of numbers 234 and 399. Show that they are relatively prime or not.

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Question

(Mid Term, Marks = 10, Lesson No. )

Show that set of provable statements in TH(N, +, x) is turing recognizable.

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