Suppose the union of the various classes of polynomial time hierarchy is defined as PH.
• There are two principal results exists. First one is based on the fact “either all or none (that is, every sparse set in PH is high or no one is low). Second one is that “No one sets will be extended high or each set of sparse will be extended high”.
• Simply, it can be said that “the hierarchy collapses in polynomial-time are the only way for simultaneous existence of high and low behaviour”.
• A disjoint set can be obtained by combining high sets and low sets. The reason behind it is “the existence of immeasurably many levels extended by the hierarchy in polynomial time and in NP there exist some sets which show neither low nor high.
Therefore, it is understood that the hierarchy in polynomial-size can be extended to only distinct finitely level if a sparse set in NP. So, we can say that the polynomial time hierarchy consists levels which are distinct and finite if PH=PSPACE.