Hardness and Hierarchy Theorems for Probabilistic Quasi-polynomial Time (Extended Abstract)

We prove tight hierarchy theorems for bounded error probabilistic quasi-polynomial time classes, under several hardness assumptions. We show that assuming either (1) the Permanent does not have subexponential time BP algorithm, or (2) some function in EXPTIME does not have subexponential size circuit, then for every 1 ff ! fi, BPTIME(2 (log d) ff ) $ BPTIME(2 (log d) fi )