Reduction from non-injective hidden shift problem to injective hidden shift problem

Mirmojtaba Gharibi

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Reduction from non-injective hidden shift problem to injective hidden shift problem

Mirmojtaba Gharibi

Quantum Physics · Submitted 19 Jul 2012

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

The authors' main claim We introduce a simple tool that can be used to reduce non-injective instances of the hidden shift problem over arbitrary group to injective instances over the same group.

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What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.05 · states quantitative result 0.06 · compares with prior results 0.88 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We introduce a simple tool that can be used to reduce non-injective instances of the hidden shift problem over arbitrary group to injective instances over the same group. In particular, we show that the average-case non-injective hidden shift problem admit this reduction. We show similar results for (non-injective) hidden shift problem for bent functions. We generalize the notion of influence and show how it relates to applicability of this tool for doing reductions. In particular, these results can be used to simplify the main results by Gavinsky, Roetteler, and Roland about the hidden shift problem for the Boolean-valued functions and bent functions, and also to generalize their results to non-Boolean domains (thereby answering an open question that they pose).

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We introduce a simple tool that can be used to reduce non-injective instances of the hidden shift problem over arbitrary group to injective instances over the same group.	contribution 0.99	0.95	0.66	asserted 0.97
s1	In particular, we show that the average-case non-injective hidden shift problem admit this reduction.	result 0.91	0.94	0.20	asserted 1.00
s2	We show similar results for (non-injective) hidden shift problem for bent functions.	result 0.81	0.94	0.11	asserted 1.00
s3	We generalize the notion of influence and show how it relates to applicability of this tool for doing reductions.	contribution 0.91	0.95	0.07	asserted 1.00
s4	In particular, these results can be used to simplify the main results by Gavinsky, Roetteler, and Roland about the hidden shift problem for the Boolean-valued functions and bent functions, and also to generalize their results to non-Boolean domains (thereby answering an open question that they pose).	interpretation 0.83	0.86	0.40	asserted 0.57

What kind of paper the classifier reports this is: method or tool 0.92 · evidence from proof or derivation 1.00.

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arXiv listing abstract v2

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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

We introduce a simple tool that can be used to reduce non-injective instances of the hidden shift problem over arbitrary group to injective instances over the same group. In particular, we show that the average-case non-injective hidden shift problem admit this reduction. We show similar results for (non-injective) hidden shift problem for bent functions. We generalize the notion of influence and show how it relates to applicability of this tool for doing reductions. In particular, these results can be used to simplify the main results by Gavinsky, Roetteler, and Roland about the hidden shift problem for the Boolean-valued functions and bent functions, and also to generalize their results to non-Boolean domains (thereby answering an open question that they pose).

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References

How the literature uses it

2 arXiv papers cite this in 6 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 3 sentences without a confident label

Compares with it 1 paper

A similar result was previously shown in a more general context by Gharibi [ref] , using a different notion of injectivisation.

Quantum pattern matching fast on average · Pattern matching in random strings · 0.86

Cites it as background 1 paper

This problem has previously been studied in [ref] .

Easy and hard functions for the Boolean hidden shift problem · Introduction · 1.00

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