A taxonomy of problems with fast parallel algorithms
Information and Control
Proc. of the conference on Structure in complexity theory
A measure of relativized space which is faithful with respect to depth
Journal of Computer and System Sciences - Structure in Complexity Theory Conference, June 2-5, 1986
Journal of Computer and System Sciences - 3rd Annual Conference on Structure in Complexity Theory, June 14–17, 1988
Bounded arithmetic, propositional logic, and complexity theory
Bounded arithmetic, propositional logic, and complexity theory
On some subrecursive reducibilities.
On some subrecursive reducibilities.
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Existing definitions of the relativizations of NC1, L and NL do not preserve the inclusions NC1 ⊆ L, NL ⊆ AC1. We start by giving the first definitions that preserve them. Here for L and NL we define their relativizations using Wilson's stack oracle model, but limit the height of the stack to a constant (instead of log(n)). We show that the collapse of any two classes in {AC0(m), TC0, NC1, L, NL} implies the collapse of their relativizations. Next we develop theories that characterize the relativizations of subclasses of P by modifying theories previously defined by the second two authors. A function is provably total in a theory iff it is in the corresponding relativized class. Finally we exhibit an oracle a that makes ACk(α) a proper hierarchy. This strengthens and clarifies the separations of the relativized theories in [Takeuti, 1995]. The idea is that a circuit whose nested depth of oracle gates is bounded by k cannot compute correctly the (k + 1) compositions of every oracle function.