The prototypical result of relativized complexity theory is the theorem of Baker, Gill and Solovay that the answer to the relativized P=? NP question depends on the oracle. Such results are commonly taken as evidence of the difficulty of solving the unrelativized case, on the assumption that simple simulations and diagonalizations generalize to oracle machines. However, some simple simulations, such as the alternation theorems of Chandra, Kozen and Stockmeyer (ALOGSPACE=P, AP=PSPACE, etc.), can fail in the presence of an oracle.
This paper examines the reasons for nonrelativizability and discusses how they can be overcome. A model for alternation oracle machines is presented in which ALOGSPACE=P and AP=PSPACE relativize to all oracles.
KeywordsConditional State Query String Query Tree Length Query Alternation Theorem
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