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a.Prove that the VC and the VCO are computationally equivalent b.Prove thatthe CLIQUE and the CLIQUEO are computationally equivalen

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a.Prove that the VC and the VCO are computationally equivalent

b.Prove thatthe CLIQUE and the CLIQUEO are computationally equivalen
Answered Same Day Dec 22, 2021

Solution

Robert answered on Dec 22 2021
127 Votes
By assuming For each variable in C that satisfies The following
F = (CX1 ∨ CX2 ∨ CX4) ∧ (CX3 ∨ CX4) ∧ (CX2 ∨ CX3) ∧ and so on

Then for each node it will be

(CX1 = 0, CX2 = 0, CX4 = 0) (CX3 = 0, CX4 = 0) (CX2 = 0, CX3 = 0) . . .
(CX1 = 0, CX2 = 1, CX4 = 0) (CX3 = 0, CX4 = 1) (CX2 = 0, CX3 = 1)
(CX1 = 0, CX2 = 1, CX4 = 1) (CX3 = 1, CX4 = 1) (CX2 = 1, CX3 = 0)
(CX1 = 1, CX2 = 0, CX4 = 0)
(CX1 = 1, CX2 = 0, CX4 = 1)
(CX1 = 1, CX2 = 1, CX4 = 0)
(CX1 = 1, CX2 = 1, CX4 = 1)



We then place a position between 2 nodes if the partial assignments square measure
consistent. Notice that the utmost doable circle size is m as a result of there are not any
edges between any 2 nodes that co
espond to an equivalent clause c. If the SAT satisfies
the assignment ,hence actually there's associate m-clique (just decide satisfies the
assignments then it will consist m nodes according...
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