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Query Order and the Polynomial Hierarchy

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Edith Hemaspaandra, Lane A. Hemaspaandra, Harald Hempel

Computational Complexity · Submitted 1 Oct 1999

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove that the levels of the polynomial hierarchy are order-oblivious.

how it is stated · asserted 1.00 read the record →

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arXiv IDcs/9910005 (version 2)
Pith IDOHRJR4EW, Pith's permanent record of this paper and its review
CitationEdith Hemaspaandra, Harald Hempel, Lane A. Hemaspaandra. "Query Order and the Polynomial Hierarchy." arXiv:cs/9910005 (1999). https://pith.science/paper/OHRJR4EW
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,235 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.94 · states limitation 0.46 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.62 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

Hemaspaandra, Hempel, and Wechsung [cs.CC/9909020] initiated the field of query order, which studies the ways in which computational power is affected by the order in which information sources are accessed. The present paper studies, for the first time, query order as it applies to the levels of the polynomial hierarchy. We prove that the levels of the polynomial hierarchy are order-oblivious. Yet, we also show that these ordered query classes form new levels in the polynomial hierarchy unless the polynomial hierarchy collapses. We prove that all leaf language classes - and thus essentially all standard complexity classes - inherit all order-obliviousness results that hold for P.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Hemaspaandra, Hempel, and Wechsung [cs.CC/9909020] initiated the field of query order, which studies the ways in which computational power is affected by the order in which information sources are accessed. background 1.00 0.03 0.02 asserted 1.00
s1 The present paper studies, for the first time, query order as it applies to the levels of the polynomial hierarchy. contribution 0.80 0.79 0.05 asserted 0.96
s2 We prove that the levels of the polynomial hierarchy are order-oblivious. result 1.00 0.95 0.70 asserted 1.00
s3 Yet, we also show that these ordered query classes form new levels in the polynomial hierarchy unless the polynomial hierarchy collapses. result 1.00 0.96 0.22 asserted 1.00
s4 We prove that all leaf language classes - and thus essentially all standard complexity classes - inherit all order-obliviousness results that hold for P. result 0.98 0.93 0.16 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

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  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Hemaspaandra, Hempel, and Wechsung [cs.CC/9909020] initiated the field of query order, which studies the ways in which computational power is affected by the order in which information sources are accessed. The present paper studies, for the first time, query order as it applies to the levels of the polynomial hierarchy. We prove that the levels of the polynomial hierarchy are order-oblivious. Yet, we also show that these ordered query classes form new levels in the polynomial hierarchy unless the polynomial hierarchy collapses. We prove 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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