NPTEL Theory of Computation Assignment 8 Answer

DecidableDecidable

 Undecidable Undecidable

Cannot be determinedCannot be determined

Turing recognisableTuring recognisable

3-SAT can be solved in polynomial time3-SAT can be solved in polynomial time

Factoring can be solved in polynomial timeFactoring can be solved in polynomial time

Halting problem can be solved in polynomial timeHalting problem can be solved in polynomial time

Graph Isomorphism can be solved in polynomial time.Graph Isomorphism can be solved in polynomial time.

A={⟨M⟩∣M is a TM and L(M) is not a finite language} A={⟨M⟩∣M is a TM and L(M) is not a finite language} 

B={⟨M⟩∣M is a TM and 11111100110∈L(M)}B={⟨M⟩∣M is a TM and 11111100110∈L(M)}

C={⟨M⟩∣M is a TM and all strings are in L(M)}C={⟨M⟩∣M is a TM and all strings are in L(M)}

None of these languagesNone of these languages

If B is regular, then A is regular.If B is regular, then A is regular.

If B is CFL, then A is CFL. If B is CFL, then A is CFL. 

 If B is Turing recognizable, then A is Turing recognizable  If B is Turing recognizable, then A is Turing recognizable 

If B is decidable, then A is decidable.If B is decidable, then A is decidable.

A is decidable.A is decidable.

 A is undecidable.  A is undecidable. 

 A¯ is Turing recognizable. A¯ is Turing recognizable.

A is regular.A is regular.

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Computable in polynomial timeComputable in polynomial time

Computable in exponential timeComputable in exponential time

Computable in non-deterministic polynomial timeComputable in non-deterministic polynomial time

UncomputableUncomputable

TrueTrue

FalseFalse

P≠NP⟹NP≠coNP P≠NP⟹NP≠coNP 

NP≠coNP⟹P≠NPNP≠coNP⟹P≠NP

NP⊆coNP⟹NP=coNPNP⊆coNP⟹NP=coNP

NP⊆coNP⟹NP≠coNP