Logical characterization of bounded query classes II: Polynomial-time oracle machines

  • Iain A. Stewart
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 702)


We have shown that the logics (±HP)*[FOS] and (±HP)1[FOS] are of the same expressibility, and both capture P NP . This result gives us the weakest possible hint that it might be wiser to try and show that (±STC*[FOS] collapses to (±STC)1[FOS] as opposed to trying to show that STC1[FOS] is closed under complementation: an attempt to use the methods of [Imm88] to achieve this latter result has failed (see [BCD89]).

As to achieving the former result, one approach might be to consider logspace DOTM's with oracles in NSYMLOG. In particular, one could try to show that such oracle machines are equivalent to logspace DOTM's which make all their oracle queries in parallel (as is the case when the oracle is in NP) and then to code such computations as formulae of DTC1[STC1[FOS]]. This is just a suggestion, but it should be clear that a consideration of oracle machines with restricted access to oracles not necessarily in NP should be undertaken.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Iain A. Stewart
    • 1
  1. 1.Computing LaboratoryUniv. Newcastle upon TyneNewcastle upon TyneEngland

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