# 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…

## 9 Citations

Equivalence Problems for Circuits over Sets of Natural Numbers

- Mathematics, Computer ScienceTheory of Computing Systems
- 2008

This work gives a systematic characterization of the complexity of equivalence problems over sets of natural numbers and provides an improved upper bound for the case of {∪,∩,−,+,×}-circuits.

A note on logspace optimization

- Computer Sciencecomputational complexity
- 2005

We show that computing iterated multiplication of word matrices over {0,1}*, using the operations maximum and concatenation, is complete for the class optL of logspace optimization functions. The…

D ec 2 01 2 On complexity of regular realizability problems ∗

- Mathematics
- 2018

A regular realizability (RR) problem is testing nonemptine ss of intersection of some fixed language (filter) with a regular language. We show t at RR problems are universal in the following sense.…

On expressive power of regular realizability problems

- MathematicsProbl. Inf. Transm.
- 2013

It is shown that RR problems are universal in the following sense: for any language L there exists an RR problem equivalent to L under disjunctive reductions in nondeterministic log space, and existence of complete problems under polynomial reductions for many complexity classes, including all classes of the polynometric hierarchy.

Reductions to Graph Isomorphism

- MathematicsTheory of Computing Systems
- 2008

It is shown that several reducibility notions coincide when applied to the Graph Isomorphism (GI) problem, and for the case of Turing reducibilities, for any k≥0 an $\textsf{NC}^{k+1}$ reduction to GI can be transformed into an $AC^{k}$ reduction to the same problem.

On complexity of regular realizability problems

- MathematicsArXiv
- 2012

Complexity of RR problems is studied to imply that for any language L there exists RR problem equivalent to L under disjunctive reductions on nondeterministic log space, and for any level of polynomial hierarchy there exists complete RR problem under polynometric reductions.

Universality of Regular Realizability Problems

- MathematicsCSR
- 2013

It is shown that RR problems are universal in the following sense: for any language L there exists an RR problem equivalent to L under disjunctive reductions on nondeterministic log space.

Multiobjective Optimization and Language Equations

- Computer Science
- 2012

A general technique is developed that helps to avoid an obstacle that is often hindering in multiobjective approximation: the problem of combining two solutions such that the new solution is balanced in all objectives and also mostly retains the structure of the original solutions.

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