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New Surprises from Self-Reducibility Eric Allender

Summary: New Surprises from Self-Reducibility
Eric Allender
Department of Computer Science, Rutgers University, Piscataway, NJ 08855,
Abstract. Self-reducibility continues to give us new angles on attacking some of
the fundamental questions about computation and complexity.
1 Introduction
Perhaps the most surprising thing about Self-Reducibility is its longevity. Who would
have suspected that this simple idea would continue to play a key role in important
developments in our evolving understanding of computation and complexity over a span
of four decades? Yet recent developments demonstrate that self-reducibility is still able
to lead us to new insights, both in computability theory and in complexity theory.
Trakhtenbrot introduced the notion of autoreducibility in a paper published forty
years ago [28]. Briefly, a set A is autoreducible if A is accepted by an oracle Turing
machine M that has A as an oracle, with the restriction that M, on input x, does not
ask its oracle about x. Already in his 1970 paper, Trakhtenbrot studied autoreducibil-
ity in the context of resource-bounded computation, although in early years the notion
was studied primarily in the context of computability [23,20]. Polynomial-time au-
toreducibility per se seems to have been studied first by Ambos-Spies [5], although
some types of polynomial-time self-reducibility (corresponding to restricted versions of


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


Collections: Computer Technologies and Information Sciences