Probabilistic computation and linear time

L. Fortnow, M. Sipser
1989 Proceedings of the twenty-first annual ACM symposium on Theory of computing - STOC '89  
In this paper, we give an oracle under which BPP is equal to probabilistic linear time, an unusual collapse of a complexity time hierarchy. In addition, we also give oracles where P 2 is contained in probabilistic linear time and where BPP has linear sized circuits, as well as oracles for the negation of these questions. This indicates that these questions will not be solved by techniques that relativize. We also note that probabilistic linear time can not contain both NP and BPP, implying that
more » ... there are languages solvable by interactive proof systems that can not be solved in probabilistic linear time.
doi:10.1145/73007.73021 dblp:conf/stoc/FortnowS89 fatcat:hxyksoak6fafpnabyotzr4xdhy