The difference hierarchy DiP is defined recursively as a D 1 P NP and b D i P A A B C for B in NP and C in D i1 P (Here B C B C ) For example, a language in D2P is the difference of two NP languages Sometimes D 2 P is called DP (and may be written D P ) Let Z G 1 , k 1 ,G 2 , k 2 G 1 has a k 1 clique and G2 doesnt have a k 2 clique Show that Z is complete for DP In other words, show that Z is in DP and every language in DP is polynomial time reducible to Z

Question: The difference hierarchy DiP is defined recursively as a. D 1 P = NP and b. D i P = {A| A = B

The difference hierarchy DiP is defined recursively as

a. D₁P = NP and

b. D_iP = {A| A = B \ C for B in NP and C in D_i−1P}.

(Here B \ C = B ∩ C.)

For example, a language in D2P is the difference of two NP languages. Sometimes D₂P is called DP (and may be written D^P). Let Z = {〈G₁, k₁,G₂, k₂〉| G₁ has a k₁-clique and G2 doesn’t have a k₂-clique}. Show that Z is complete for DP. In other words, show that Z is in DP and every language in DP is polynomial time reducible to Z.

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