An oracle builder's toolkit

  • Authors:

  • Stephen Fenner;Lance Fortnow;Stuart A. Kurtz;Lide Li

  • Affiliations:

  • Department of Computer Science, University of Chicago, 1100 East 58th St., Chicago, IL;Department of Computer Science, University of Chicago, 1100 East 58th St., Chicago, IL;Department of Computer Science, University of Chicago, 1100 East 58th St., Chicago, IL;Department of Computer Science, University of Chicago, 1100 East 58th St., Chicago, IL

  • Venue:
  • Information and Computation
  • Year:
  • 2003

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Abstract

We show how to use various notions of genericity as tools in oracle creation. In particular, 1. we give an abstract definition of genericity that encompasses a large collection of different generic notions; 2. we consider a new complexity class AWPP , which contains BQP (quantum polynomial time), and infer several strong collapses relative to SP -generics; 3. we show that under additional assumptions these collapses also occur relative to Cohen generics; 4. we show that relative to SP -generics, ULIN ∩ co- ULIN ⊈ DTIME ( n k ) for any k , where ULIN is unambiguous linear time, despite the fact that UP ∪ ( NP ∩ co- NP ) ⊆ P relative to these generics; 5. we show that there is an oracle relative to which NP/1 ∩ co- NP/1 ⊈ ( NP ∩ co- NP )/ poly ; and 6. we use a specialized notion of genericity to create an oracle relative to which NP BPP ⊉MA .