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Oracles versus Proof Techniques that Do Not Relativize1 Eric Allender2

Summary: Oracles versus Proof Techniques that Do Not Relativize1
Eric Allender2
Department of Computer Science
Rutgers University
New Brunswick, NJ 08903
ABSTRACT Oracle constructions have long been used to provide evidence that cer-
tain questions in complexity theory cannot be resolved using the usual techniques of sim-
ulation and diagonalization. However, the existence of nonrelativizing proof techniques
seems to call this practice into question. This paper reviews the status of nonrelativizing
proof techniques, and argues that many oracle constructions still yield valuable informa-
tion about problems in complexity theory.
1 Introduction
One of the most exciting theorems of this past winter was proved by Adi Shamir in
[Sh-89], where it is shown that PSPACE is the class of sets having interactive proof
systems. This result is significant for many reasons, but this paper will focus on one
aspect of this work: it does not relativize. The results of [Sh-89], along with the related
work of [LFKN-89, BFL-90], are the first truly compelling examples of theorems about
complexity classes that are known to be true in the unrelativized case, but are false
relative to some oracles.
Of course, other examples of nonrelativizing proof techniques have been known for


Source: Allender, Eric - Department of Computer Science, Rutgers University


Collections: Computer Technologies and Information Sciences