4 Search Results for "Dwivedi, Ashish"

Document
DOI: 10.4230/LIPIcs.CCC.2025.1
List Decoding Quotient Reed-Muller Codes

Authors: Omri Gotlib, Tali Kaufman, and Shachar Lovett

Published in: LIPIcs, Volume 339, 40th Computational Complexity Conference (CCC 2025)

Abstract
Reed-Muller codes consist of evaluations of n-variate polynomials over a finite field 𝔽 with degree at most d. Much like every linear code, Reed-Muller codes can be characterized by constraints, where a codeword is valid if and only if it satisfies all degree-d constraints. For a subset X̃ ⊆ 𝔽ⁿ, we introduce the notion of X̃-quotient Reed-Muller code. A function F:X̃ → 𝔽 is a valid codeword in the quotient code if it satisfies all the constraints of degree-d polynomials lying in X̃. This gives rise to a novel phenomenon: a quotient codeword may have many extensions to original codewords. This weakens the connection between original codewords and quotient codewords which introduces a richer range of behaviors along with substantial new challenges. Our goal is to answer the following question: what properties of X̃ will imply that the quotient code inherits its distance and list-decoding radius from the original code? We address this question using techniques developed by Bhowmick and Lovett [Abhishek Bhowmick and Shachar Lovett, 2014], identifying key properties of 𝔽ⁿ used in their proof and extending them to general subsets X̃ ⊆ 𝔽ⁿ. By introducing a new tool, we overcome the novel challenge in analyzing the quotient code that arises from the weak connection between original and quotient codewords. This enables us to apply known results from additive combinatorics and algebraic geometry [David Kazhdan and Tamar Ziegler, 2018; David Kazhdan and Tamar Ziegler, 2019; Amichai Lampert and Tamar Ziegler, 2021] to show that when X̃ is a high rank variety, X̃-quotient Reed-Muller codes inherit the distance and list-decoding parameters from the original Reed-Muller codes.
Cite as

Omri Gotlib, Tali Kaufman, and Shachar Lovett. List Decoding Quotient Reed-Muller Codes. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 1:1-1:44, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{gotlib_et_al:LIPIcs.CCC.2025.1,
  author =	{Gotlib, Omri and Kaufman, Tali and Lovett, Shachar},
  title =	{{List Decoding Quotient Reed-Muller Codes}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{1:1--1:44},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.1},
  URN =		{urn:nbn:de:0030-drops-236957},
  doi =		{10.4230/LIPIcs.CCC.2025.1},
  annote =	{Keywords: Reed-Muller Codes, Quotient Code, Quotient Reed-Muller Code, List Decoding, High Rank Variety, High-Order Fourier Analysis, Error-Correcting Codes}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.44
Optimal Pseudorandom Generators for Low-Degree Polynomials over Moderately Large Fields

Authors: Ashish Dwivedi, Zeyu Guo, and Ben Lee Volk

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
We construct explicit pseudorandom generators that fool n-variate polynomials of degree at most d over a finite field 𝔽_q. The seed length of our generators is O(d log n + log q), over fields of size exponential in d and characteristic at least d(d-1)+1. Previous constructions such as Bogdanov’s (STOC 2005) and Derksen and Viola’s (FOCS 2022) had either suboptimal seed length or required the field size to depend on n. Our approach follows Bogdanov’s paradigm while incorporating techniques from Lecerf’s factorization algorithm (J. Symb. Comput. 2007) and insights from the construction of Derksen and Viola regarding the role of indecomposability of polynomials.
Cite as

Ashish Dwivedi, Zeyu Guo, and Ben Lee Volk. Optimal Pseudorandom Generators for Low-Degree Polynomials over Moderately Large Fields. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 44:1-44:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{dwivedi_et_al:LIPIcs.APPROX/RANDOM.2024.44,
  author =	{Dwivedi, Ashish and Guo, Zeyu and Volk, Ben Lee},
  title =	{{Optimal Pseudorandom Generators for Low-Degree Polynomials over Moderately Large Fields}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{44:1--44:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.44},
  URN =		{urn:nbn:de:0030-drops-210370},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.44},
  annote =	{Keywords: Pseudorandom Generators, Low Degree Polynomials}
}
Document
Vision
DOI: 10.4230/TGDK.1.1.3
Knowledge Engineering Using Large Language Models

Authors: Bradley P. Allen, Lise Stork, and Paul Groth

Published in: TGDK, Volume 1, Issue 1 (2023): Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge, Volume 1, Issue 1

Abstract
Knowledge engineering is a discipline that focuses on the creation and maintenance of processes that generate and apply knowledge. Traditionally, knowledge engineering approaches have focused on knowledge expressed in formal languages. The emergence of large language models and their capabilities to effectively work with natural language, in its broadest sense, raises questions about the foundations and practice of knowledge engineering. Here, we outline the potential role of LLMs in knowledge engineering, identifying two central directions: 1) creating hybrid neuro-symbolic knowledge systems; and 2) enabling knowledge engineering in natural language. Additionally, we formulate key open research questions to tackle these directions.
Cite as

Bradley P. Allen, Lise Stork, and Paul Groth. Knowledge Engineering Using Large Language Models. In Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge (TGDK), Volume 1, Issue 1, pp. 3:1-3:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@Article{allen_et_al:TGDK.1.1.3,
  author =	{Allen, Bradley P. and Stork, Lise and Groth, Paul},
  title =	{{Knowledge Engineering Using Large Language Models}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{3:1--3:19},
  ISSN =	{2942-7517},
  year =	{2023},
  volume =	{1},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.1.1.3},
  URN =		{urn:nbn:de:0030-drops-194777},
  doi =		{10.4230/TGDK.1.1.3},
  annote =	{Keywords: knowledge engineering, large language models}
}
Document
DOI: 10.4230/LIPIcs.CCC.2019.15
Counting Basic-Irreducible Factors Mod p^k in Deterministic Poly-Time and p-Adic Applications

Authors: Ashish Dwivedi, Rajat Mittal, and Nitin Saxena

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

Abstract
Finding an irreducible factor, of a polynomial f(x) modulo a prime p, is not known to be in deterministic polynomial time. Though there is such a classical algorithm that counts the number of irreducible factors of f mod p. We can ask the same question modulo prime-powers p^k. The irreducible factors of f mod p^k blow up exponentially in number; making it hard to describe them. Can we count those irreducible factors mod p^k that remain irreducible mod p? These are called basic-irreducible. A simple example is in f=x^2+px mod p^2; it has p many basic-irreducible factors. Also note that, x^2+p mod p^2 is irreducible but not basic-irreducible! We give an algorithm to count the number of basic-irreducible factors of f mod p^k in deterministic poly(deg(f),k log p)-time. This solves the open questions posed in (Cheng et al, ANTS'18 & Kopp et al, Math.Comp.'19). In particular, we are counting roots mod p^k; which gives the first deterministic poly-time algorithm to compute Igusa zeta function of f. Also, our algorithm efficiently partitions the set of all basic-irreducible factors (possibly exponential) into merely deg(f)-many disjoint sets, using a compact tree data structure and split ideals.
Cite as

Ashish Dwivedi, Rajat Mittal, and Nitin Saxena. Counting Basic-Irreducible Factors Mod p^k in Deterministic Poly-Time and p-Adic Applications. In 34th Computational Complexity Conference (CCC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 137, pp. 15:1-15:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{dwivedi_et_al:LIPIcs.CCC.2019.15,
  author =	{Dwivedi, Ashish and Mittal, Rajat and Saxena, Nitin},
  title =	{{Counting Basic-Irreducible Factors Mod p^k in Deterministic Poly-Time and p-Adic Applications}},
  booktitle =	{34th Computational Complexity Conference (CCC 2019)},
  pages =	{15:1--15:29},
  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.2019.15},
  URN =		{urn:nbn:de:0030-drops-108373},
  doi =		{10.4230/LIPIcs.CCC.2019.15},
  annote =	{Keywords: deterministic, root, counting, modulo, prime-power, tree, basic irreducible, unramified}
}
  • Refine by Type
  • 4 Document/PDF
  • 2 Document/HTML

  • Refine by Publication Year
  • 1 2025
  • 1 2024
  • 1 2023
  • 1 2019

  • Refine by Author
  • 2 Dwivedi, Ashish
  • 1 Allen, Bradley P.
  • 1 Gotlib, Omri
  • 1 Groth, Paul
  • 1 Guo, Zeyu
  • Show More...

  • Refine by Series/Journal
  • 3 LIPIcs
  • 1 TGDK

  • Refine by Classification
  • 2 Theory of computation → Pseudorandomness and derandomization
  • 1 Computing methodologies → Hybrid symbolic-numeric methods
  • 1 Computing methodologies → Machine learning
  • 1 Computing methodologies → Natural language processing
  • 1 Computing methodologies → Number theory algorithms
  • Show More...

  • Refine by Keyword
  • 1 Error-Correcting Codes
  • 1 High Rank Variety
  • 1 High-Order Fourier Analysis
  • 1 List Decoding
  • 1 Low Degree Polynomials
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact