LECTURE 2-7 Complete Problems in PH

THEOREM PROOF

BOUNDED HALTING PROBLEM (BHP) THEOREM PROOF

A BHP LEMMA PROOF

LEMMA PROOF

DEFINITION THEOREM PROOF by induction on k

Machine Related Problem Natural Problem (Machine unrelated) Machine Related Problem

SAT k THEOREM

PROOF (odd k)

3-CNF SAT k THEOREM

Generalized Ramsey Number

THEOREM PROOF Construction Such that

Variables

Variables Clauses

Variables Clauses

Variables Clauses

Variables Clauses

Variables Clauses

Variables Clauses

Variables Clauses

Case 1 Answer:

Case 2 Answer:

Case 2 Answer:

Consider To prove Define a coloring c’: No red clique of size K exists.

Consider To prove Define a coloring c’: No red clique of size K exists. There must exist a blue clique Q of size K.

PPROPERTY OF BLUE CLIQUE Q Assignment for y Then F(X,Y) is satisfied

Thanks, end.