clarke@utcsri.UUCP (06/04/87)
THEORY SEMINAR, Thursday, June 11, 3 pm, GB120 (GB = Galbraith Building, 35 St. George Street) Professor Lane A. Hemachandra Cornell University ``THE SKY IS FALLING: The Strong Exponential Hierarchy Collapses" The polynomial hierarchy plays a dominant role in classifying the complex- ity of feasible computations. Composed of the levels P, NP, NP(NP) , etc., the grand obsession of complexity theory is to discover whether these levels collapse. This goal is reflected in our romantic fixation on the P=NP question. Love, devotion, and NSF grants notwithstanding, the ques- tion of the the collapse of the polynomial hierarchy continues to defy solution, and may lie beyond the scope of current mathematical proof tech- niques. We resolve the question of collapse for an exponential analogue of the polynomial hierarchy. Composed of the levels E, NE, NP(NE), etc., the strong exponential hierarchy collapses to P(NE): P(NE)=NP(NE)! Our proof stresses the use of partial census information and the extraordinary exploitation of nondeterminism. We survey recent related results in structural complexity that also spotlight counting. -- Jim Clarke -- Dept. of Computer Science, Univ. of Toronto, Canada M5S 1A4 (416) 978-4058 {allegra,cornell,decvax,linus,utzoo}!utcsri!clarke