2 Search Results for "Yitayew, Michael A."

Document

DOI: 10.4230/LIPIcs.ITCS.2025.90

Polynomial Size, Short-Circuit Resilient Circuits for NC

Authors: Yael Tauman Kalai and Raghuvansh R. Saxena

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract

We show how to convert any circuit of poly-logarithmic depth and polynomial size into a functionally equivalent circuit of polynomial size (and polynomial depth) that is resilient to adversarial short-circuit errors. Specifically, the resulting circuit computes the same function even if up to ε d gates on every root-to-leaf path are short-circuited, i.e., their output is replaced with the value of one of its inputs, where d is the depth of the circuit and ε > 0 is a fixed constant. Previously, such a result was known for formulas (Kalai-Lewko-Rao, FOCS 2012). It was also known how to convert general circuits to error resilient ones whose size is quasi-polynomial in the size of the original circuit (Efremenko et al. STOC 2022). The reason both these works do not extend to our setting is that there may be many paths from the root to a given gate, and the resilient circuits needs to "remember" a lot of information about these paths, which causes it to be large. Our main idea is to reduce the amount of this information at the cost of increasing the depth of the resilient circuit.

Cite as

Yael Tauman Kalai and Raghuvansh R. Saxena. Polynomial Size, Short-Circuit Resilient Circuits for NC. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 90:1-90:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{taumankalai_et_al:LIPIcs.ITCS.2025.90,
  author =	{Tauman Kalai, Yael and Saxena, Raghuvansh R.},
  title =	{{Polynomial Size, Short-Circuit Resilient Circuits for NC}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{90:1--90:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.90},
  URN =		{urn:nbn:de:0030-drops-227181},
  doi =		{10.4230/LIPIcs.ITCS.2025.90},
  annote =	{Keywords: Error-resilient computation, short-circuit errors}
}

Document

DOI: 10.4230/LIPIcs.CCC.2019.10

Optimal Short-Circuit Resilient Formulas

Authors: Mark Braverman, Klim Efremenko, Ran Gelles, and Michael A. Yitayew

Published in: LIPIcs, Volume 137, 34th Computational Complexity Conference (CCC 2019)

Abstract

We consider fault-tolerant boolean formulas in which the output of a faulty gate is short-circuited to one of the gate’s inputs. A recent result by Kalai et al. [FOCS 2012] converts any boolean formula into a resilient formula of polynomial size that works correctly if less than a fraction 1/6 of the gates (on every input-to-output path) are faulty. We improve the result of Kalai et al., and show how to efficiently fortify any boolean formula against a fraction 1/5 of short-circuit gates per path, with only a polynomial blowup in size. We additionally show that it is impossible to obtain formulas with higher resilience and sub-exponential growth in size. Towards our results, we consider interactive coding schemes when noiseless feedback is present; these produce resilient boolean formulas via a Karchmer-Wigderson relation. We develop a coding scheme that resists up to a fraction 1/5 of corrupted transmissions in each direction of the interactive channel. We further show that such a level of noise is maximal for coding schemes with sub-exponential blowup in communication. Our coding scheme takes a surprising inspiration from Blockchain technology.

Cite as

Mark Braverman, Klim Efremenko, Ran Gelles, and Michael A. Yitayew. Optimal Short-Circuit Resilient Formulas. In 34th Computational Complexity Conference (CCC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 137, pp. 10:1-10:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{braverman_et_al:LIPIcs.CCC.2019.10,
  author =	{Braverman, Mark and Efremenko, Klim and Gelles, Ran and Yitayew, Michael A.},
  title =	{{Optimal Short-Circuit Resilient Formulas}},
  booktitle =	{34th Computational Complexity Conference (CCC 2019)},
  pages =	{10:1--10:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-116-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{137},
  editor =	{Shpilka, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2019.10},
  URN =		{urn:nbn:de:0030-drops-108326},
  doi =		{10.4230/LIPIcs.CCC.2019.10},
  annote =	{Keywords: Circuit Complexity, Noise-Resilient Circuits, Interactive Coding, Coding Theory, Karchmer-Wigderson Games}
}

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2 Search Results for "Yitayew, Michael A."

Polynomial Size, Short-Circuit Resilient Circuits for NC

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Optimal Short-Circuit Resilient Formulas

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