# Commutative queries

@article{Beigel1997CommutativeQ, title={Commutative queries}, author={Richard Beigel and Richard Chang}, journal={Proceedings of the Fifth Israeli Symposium on Theory of Computing and Systems}, year={1997}, pages={159-165} }

We consider polynomial-time Turing machines that have access to two oracles and investigate when the order of oracle queries is significant. The oracles used here are complete languages for the Polynomial Hierarchy (PH). We prove that, for solving decision problems, the order of oracle queries does not matter. This improves upon the previous result of Hemaspaandra, Hemaspaandra and Hempel, who showed that the order of the queries does not matter if the base machine asks only one query to each…

## 12 Citations

### Query Order and the Polynomial Hierarchy

- Computer Science, MathematicsJ. Univers. Comput. Sci.
- 1998

It is proved that all leaf language classes - and thus essentially all standard complexity classes - inherit all order-obliviousness results that hold for P. complexity levels, and it is shown that these ordered query classes form new levels in the polynomial hierarchy unless the poynomial hierarchy collapses.

### An Introduction to Query Order

- Computer ScienceBull. EATCS
- 1997

The study of query order has yielded dividends in seemingly unrelated areas, such as bottleneck computations and downward translation of equality, and some of the central results are presented.

### R1-ttSN(NP) Distinguishes Robust Many-One and Turing Completeness

- MathematicsArXiv
- 1999

It is proved that a relatively natural complexity class, \rsnnp - a downward closure of NP, has Turing-complete sets but has no many-one complete sets, and it is shown that in the same relativized world this class has 2-truth-table complete sets but lacks 1- Truth- table complete sets.

### Bounded Queries, Approximations, and the Boolean Hierarchy

- Computer ScienceInf. Comput.
- 1997

This paper investigates nondeterministic bounded query classes in relation to the complexity of NP-hard approximation problems and the Boolean Hierarchy and proves that in many cases, NP-approximation problems have the upward collapse property.

### Query Order in the Polynomial Hierarchy

- Computer Science, MathematicsFCT
- 1997

It is proved that all leaf language classes---and thus essentially all standard complexity classes---inherit all order-obliviousness results that hold for P.

### On the commutativity of jumps

- MathematicsJournal of Symbolic Logic
- 2000

It is shown that if A1 ….. Ak are jumps that are not too close together, then all three of these classes are identical and are not changed if the authors permute (r1…..rkAk).

### Self-Specifying Machines

- MathematicsInt. J. Found. Comput. Sci.
- 1999

The computational power of machines that specify their own acceptance types are studied, and it is shown that they accept exactly the languages in R^(#P)_m(NP).

### RSN1-tt(NP) Distinguishes Robust Many-One and Turing Completeness

- Computer ScienceTheory of Computing Systems
- 1998

It is proved that a relatively natural complexity class, a downward closure of NP, has many equivalent forms having to do with ordered and parallel access to NP and NP ∩ coNP.

### The Computational Complexity Column

- Computer Science, Mathematics
- 1998

Williams' proof that NEXP 6⊆ ACC proceeds via a new algorithm for ACC-SAT beating brute-force search is the centrepiece of the article, which exploits a formal connection from non-trivial SAT algorithms to circuit lower bounds.

### A Note on Parallel Queries and the Symmetric-Difference Hierarchy

- MathematicsInf. Process. Lett.
- 1998

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This paper investigates nondeterministic bounded query classes in relation to the complexity of NP-hard approximation problems and the Boolean Hierarchy and proves that in many cases, NP-approximation problems have the upward collapse property.

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It is proved that all leaf language classes---and thus essentially all standard complexity classes---inherit all order-obliviousness results that hold for P.

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