Adaptive logspace reducibility and parallel time

@article{lvarez2005AdaptiveLR,
  title={Adaptive logspace reducibility and parallel time},
  author={Carme {\`A}lvarez and Jos{\'e} Lu{\'i}s Balc{\'a}zar and Birgit Jenner},
  journal={Mathematical systems theory},
  year={2005},
  volume={28},
  pages={117-140}
}
We discuss two notions of functional oracle for logarithmic space-bounded machines, which differ in whether there is only one oracle tape for both the query and the answer or a separate tape for the answer, which can still be read while the next query is already being constructed. The first notion turns out to be basically nonadaptive, behaving like access to an oracle set. The second notion, on the other hand, is adaptive. By imposing appropriate bounds on the number of functional oracle… 
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References

SHOWING 1-10 OF 25 REFERENCES
Bounded Query Classes
TLDR
The Boolean hierarchy is generalized in such a way that it is possible to characterize P and O in terms of the generalization, and the class $P^{\text{NP}}[O(\log n)]$ can be characterized in very different ways.
Relativization of questions about log space computability
TLDR
A notion of log space Turing reducibility is introduced and it is shown that there exists a computable setA such that and.
A very hard log space counting class
  • C. Àlvarez, Birgit Jenner
  • Computer Science, Mathematics
    Proceedings Fifth Annual Structure in Complexity Theory Conference
  • 1990
TLDR
It is demonstrated that span-L-functions can be computed in polynomial time if and only if P=NP=PH=P( Hash P), i.e if the class P(Hash P) and all the classes of thePolynomial-time hierarchy are contained in P.
Two applications of complementation via inductive counting
TLDR
An errorless probabilistic algorithm is given for the undirected graph s-t connectivity problem that runs in O(log n) space and polynomial expected time, and it is shown that the class LOGCFL is closed under complementation.
Comparison of polynomial-time reducibilities
TLDR
Comparison of the polynomial-time-bounded reducibilities introduced by Cook [1] and Karp] leads naturally to the definition of several intermediate truth-tableredcibilities, and it is noted that all redu cibilities of this type which do not have obvious implication relationships are in fact distinct in a strong sense.
On uniform circuit complexity
  • W. L. Ruzzo
  • Computer Science
    20th Annual Symposium on Foundations of Computer Science (sfcs 1979)
  • 1979
On truth-table reducibility to SAT and the difference hierarchy over NP
  • S. Buss, L. Hay
  • Computer Science
    [1988] Proceedings. Structure in Complexity Theory Third Annual Conference
  • 1988
It is shown that polynomial-time truth-table reducibility by Boolean circuits to SAT is the same as log-space truth-table reducibility via Boolean formulas to SAT and the same as log-space Turing
Two Applications of Inductive Counting for Complementation Problems
TLDR
It is shown that small numbers of “role switches” in two- person pebbling can be eliminated and a general result that shows closure under complementation of classes defined by semi-unbounded fan-in circuits is shown.
A Taxonomy of Problems with Fast Parallel Algorithms
  • S. Cook
  • Computer Science, Mathematics
    Inf. Control.
  • 1985
The complexity of optimization problems
TLDR
The central result is that any FPSAT function decomposes into an OptP function followed by polynomial-time computation, and it quantifies "how much" NP-completeness is in a problem, i.e., the number of NP queries it takes to compute the function.
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