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Documents authored by Kindler, Guy

Document
DOI: 10.4230/LIPIcs.ITCS.2023.25
Improved Monotonicity Testers via Hypercube Embeddings

Authors: Mark Braverman, Subhash Khot, Guy Kindler, and Dor Minzer

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
We show improved monotonicity testers for the Boolean hypercube under the p-biased measure, as well as over the hypergrid [m]ⁿ. Our results are: 1) For any p ∈ (0,1), for the p-biased hypercube we show a non-adaptive tester that makes Õ(√n/ε²) queries, accepts monotone functions with probability 1 and rejects functions that are ε-far from monotone with probability at least 2/3. 2) For all m ∈ ℕ, we show an Õ(√nm³/ε²) query monotonicity tester over [m]ⁿ. We also establish corresponding directed isoperimetric inequalities in these domains, analogous to the isoperimetric inequality in [Subhash Khot et al., 2018]. Previously, the best known tester due to Black, Chakrabarty and Seshadhri [Hadley Black et al., 2018] had Ω(n^{5/6}) query complexity. Our results are optimal up to poly-logarithmic factors and the dependency on m. Our proof uses a notion of monotone embeddings of measures into the Boolean hypercube that can be used to reduce the problem of monotonicity testing over an arbitrary product domains to the Boolean cube. The embedding maps a function over a product domain of dimension n into a function over a Boolean cube of a larger dimension n', while preserving its distance from being monotone; an embedding is considered efficient if n' is not much larger than n, and we show how to construct efficient embeddings in the above mentioned settings.
Cite as

Mark Braverman, Subhash Khot, Guy Kindler, and Dor Minzer. Improved Monotonicity Testers via Hypercube Embeddings. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 25:1-25:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{braverman_et_al:LIPIcs.ITCS.2023.25,
  author =	{Braverman, Mark and Khot, Subhash and Kindler, Guy and Minzer, Dor},
  title =	{{Improved Monotonicity Testers via Hypercube Embeddings}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{25:1--25:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.25},
  URN =		{urn:nbn:de:0030-drops-175285},
  doi =		{10.4230/LIPIcs.ITCS.2023.25},
  annote =	{Keywords: Property Testing, Monotonicity Testing, Isoperimetric Inequalities}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2021.26
Theorems of KKL, Friedgut, and Talagrand via Random Restrictions and Log-Sobolev Inequality

Authors: Esty Kelman, Subhash Khot, Guy Kindler, Dor Minzer, and Muli Safra

Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)

Abstract
We give alternate proofs for three related results in analysis of Boolean functions, namely the KKL Theorem, Friedgut’s Junta Theorem, and Talagrand’s strengthening of the KKL Theorem. We follow a new approach: looking at the first Fourier level of the function after a suitable random restriction and applying the Log-Sobolev inequality appropriately. In particular, we avoid using the hypercontractive inequality that is common to the original proofs. Our proofs might serve as an alternate, uniform exposition to these theorems and the techniques might benefit further research.
Cite as

Esty Kelman, Subhash Khot, Guy Kindler, Dor Minzer, and Muli Safra. Theorems of KKL, Friedgut, and Talagrand via Random Restrictions and Log-Sobolev Inequality. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 26:1-26:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{kelman_et_al:LIPIcs.ITCS.2021.26,
  author =	{Kelman, Esty and Khot, Subhash and Kindler, Guy and Minzer, Dor and Safra, Muli},
  title =	{{Theorems of KKL, Friedgut, and Talagrand via Random Restrictions and Log-Sobolev Inequality}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{26:1--26:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{Lee, James R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.26},
  URN =		{urn:nbn:de:0030-drops-135657},
  doi =		{10.4230/LIPIcs.ITCS.2021.26},
  annote =	{Keywords: Fourier Analysis, Hypercontractivity, Log-Sobolev Inequality}
}
Document
DOI: 10.4230/LIPIcs.CCC.2020.17
Limits of Preprocessing

Authors: Yuval Filmus, Yuval Ishai, Avi Kaplan, and Guy Kindler

Published in: LIPIcs, Volume 169, 35th Computational Complexity Conference (CCC 2020)

Abstract
It is a classical result that the inner product function cannot be computed by an AC⁰ circuit [Merrick L. Furst et al., 1981; Miklós Ajtai, 1983; Johan Håstad, 1986]. It is conjectured that this holds even if we allow arbitrary preprocessing of each of the two inputs separately. We prove this conjecture when the preprocessing of one of the inputs is limited to output n + n/(log^{ω(1)} n) bits. Our methods extend to many other functions, including pseudorandom functions, and imply a (weak but nontrivial) limitation on the power of encoding inputs in low-complexity cryptography. Finally, under cryptographic assumptions, we relate the question of proving variants of the main conjecture with the question of learning AC⁰ under simple input distributions.
Cite as

Yuval Filmus, Yuval Ishai, Avi Kaplan, and Guy Kindler. Limits of Preprocessing. In 35th Computational Complexity Conference (CCC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 169, pp. 17:1-17:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{filmus_et_al:LIPIcs.CCC.2020.17,
  author =	{Filmus, Yuval and Ishai, Yuval and Kaplan, Avi and Kindler, Guy},
  title =	{{Limits of Preprocessing}},
  booktitle =	{35th Computational Complexity Conference (CCC 2020)},
  pages =	{17:1--17:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-156-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{169},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2020.17},
  URN =		{urn:nbn:de:0030-drops-125697},
  doi =		{10.4230/LIPIcs.CCC.2020.17},
  annote =	{Keywords: circuit, communication complexity, IPPP, preprocessing, PRF, simultaneous messages}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.15
Quantum Automata Cannot Detect Biased Coins, Even in the Limit

Authors: Guy Kindler and Ryan O'Donnell

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Abstract
Aaronson and Drucker (2011) asked whether there exists a quantum finite automaton that can distinguish fair coin tosses from biased ones by spending significantly more time in accepting states, on average, given an infinite sequence of tosses. We answer this question negatively.
Cite as

Guy Kindler and Ryan O'Donnell. Quantum Automata Cannot Detect Biased Coins, Even in the Limit. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 15:1-15:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{kindler_et_al:LIPIcs.ICALP.2017.15,
  author =	{Kindler, Guy and O'Donnell, Ryan},
  title =	{{Quantum Automata Cannot Detect Biased Coins, Even in the Limit}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{15:1--15:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.15},
  URN =		{urn:nbn:de:0030-drops-73995},
  doi =		{10.4230/LIPIcs.ICALP.2017.15},
  annote =	{Keywords: quantum automata}
}
Document
DOI: 10.4230/LIPIcs.CCC.2016.15
Invariance Principle on the Slice

Authors: Yuval Filmus, Guy Kindler, Elchanan Mossel, and Karl Wimmer

Published in: LIPIcs, Volume 50, 31st Conference on Computational Complexity (CCC 2016)

Abstract
We prove a non-linear invariance principle for the slice. As applications, we prove versions of Majority is Stablest, Bourgain's tail theorem, and the Kindler-Safra theorem for the slice. From the latter we deduce a stability version of the t-intersecting Erdos-Ko-Rado theorem.
Cite as

Yuval Filmus, Guy Kindler, Elchanan Mossel, and Karl Wimmer. Invariance Principle on the Slice. In 31st Conference on Computational Complexity (CCC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 50, pp. 15:1-15:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{filmus_et_al:LIPIcs.CCC.2016.15,
  author =	{Filmus, Yuval and Kindler, Guy and Mossel, Elchanan and Wimmer, Karl},
  title =	{{Invariance Principle on the Slice}},
  booktitle =	{31st Conference on Computational Complexity (CCC 2016)},
  pages =	{15:1--15:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-008-8},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{50},
  editor =	{Raz, Ran},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2016.15},
  URN =		{urn:nbn:de:0030-drops-58236},
  doi =		{10.4230/LIPIcs.CCC.2016.15},
  annote =	{Keywords: analysis of boolean functions, invariance principle, Johnson association scheme, the slice}
}
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