25 Search Results for "Guo, Zeyu"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.49
Debordering Closure Results in Determinantal and Pfaffian Ideals

Authors: Anakin Dey and Zeyu Guo

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
One important question in algebraic complexity is understanding the complexity of polynomial ideals (Grochow, Bulletin of EATCS 131, 2020). Andrews and Forbes (STOC 2022) studied the determinantal ideals I^{det}_{n,m,r} generated by the r× r minors of n× m matrices. Over fields of characteristic zero or of sufficiently large characteristic, they showed that for any nonzero f ∈ I^{det}_{n,m,r}, the determinant of a t × t matrix of variables with t = Θ{r^{1/3}} is approximately computed by a constant-depth, polynomial-size f-oracle algebraic circuit, in the sense that the determinant lies in the border of such circuits. An analogous result was also obtained for Pfaffians in the same paper. In this work, we deborder the result of Andrews and Forbes by showing that when f has polynomial degree, the determinant is in fact exactly computed by a constant-depth, polynomial-size f-oracle algebraic circuit. We further establish an analogous result for Pfaffian ideals. Our results are established using the isolation lemma, combined with a careful analysis of straightening-law expansions of polynomials in determinantal and Pfaffian ideals.
Cite as

Anakin Dey and Zeyu Guo. Debordering Closure Results in Determinantal and Pfaffian Ideals. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 49:1-49:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{dey_et_al:LIPIcs.ITCS.2026.49,
  author =	{Dey, Anakin and Guo, Zeyu},
  title =	{{Debordering Closure Results in Determinantal and Pfaffian Ideals}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{49:1--49:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.49},
  URN =		{urn:nbn:de:0030-drops-253363},
  doi =		{10.4230/LIPIcs.ITCS.2026.49},
  annote =	{Keywords: Algebraic circuit complexity, Isolation lemma, Debordering}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.9
On Closure Properties of Read-Once Oblivious Algebraic Branching Programs

Authors: Robert Andrews, Jules Armand, Prateek Dwivedi, Magnus Rahbek Dalgaard Hansen, Nutan Limaye, Srikanth Srinivasan, and Sébastien Tavenas

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We investigate the closure properties of read-once oblivious Algebraic Branching Programs (roABPs) under various natural algebraic operations and prove the following. - Non-closure under factoring: There is a sequence of explicit polynomials (f_n(x₁,…, x_n))_n that have poly(n)-sized roABPs such that some irreducible factor of f_n requires roABPs of superpolynomial size in any order. - Non-closure under powering: There is a sequence of polynomials (f_n(x₁,…, x_n))_n with poly(n)-sized roABPs such that any super-constant power of f_n does not have roABPs of polynomial size in any order (and f_nⁿ requires exponential size in any order). - Non-closure under symmetric operations: There are symmetric polynomials (f_n(e₁,…, e_n))_n that have roABPs of polynomial size such that f_n(x₁,…, x_n) do not have roABPs of subexponential size. (Here, e₁,…, e_n denote the elementary symmetric polynomials in n variables.) These results should be viewed in light of known results on models such as algebraic circuits, (general) algebraic branching programs, formulas and constant-depth circuits, all of which are known to be closed under these operations. To prove non-closure under factoring, we construct hard polynomials based on expander graphs using gadgets that lift their hardness from sparse polynomials to roABPs. For symmetric compositions, we show that the circulant polynomial requires roABPs of exponential size in every variable order.
Cite as

Robert Andrews, Jules Armand, Prateek Dwivedi, Magnus Rahbek Dalgaard Hansen, Nutan Limaye, Srikanth Srinivasan, and Sébastien Tavenas. On Closure Properties of Read-Once Oblivious Algebraic Branching Programs. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 9:1-9:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{andrews_et_al:LIPIcs.ITCS.2026.9,
  author =	{Andrews, Robert and Armand, Jules and Dwivedi, Prateek and Hansen, Magnus Rahbek Dalgaard and Limaye, Nutan and Srinivasan, Srikanth and Tavenas, S\'{e}bastien},
  title =	{{On Closure Properties of Read-Once Oblivious Algebraic Branching Programs}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{9:1--9:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.9},
  URN =		{urn:nbn:de:0030-drops-252964},
  doi =		{10.4230/LIPIcs.ITCS.2026.9},
  annote =	{Keywords: Factoring, Closure Properties, Sparsity Bounds, Symmetric Polynomials, roABP, Expander Graphs}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.116
Decentralized Data Archival: New Definitions and Constructions

Authors: Elaine Shi, Rose Silver, and Changrui Mu

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We initiate the study of a new abstraction called incremental decentralized data archival (iDDA). Specifically, imagine that there is an ever-growing, massive database such as a blockchain, a comprehensive human knowledge base like Wikipedia, or the Internet archive. We want to build a decentralized archival system for such datasets to ensure long-term robustness and sustainability. We identify several important properties that an iDDA scheme should satisfy. First, to promote heterogeneity and decentralization, we want to encourage even weak nodes with limited space (e.g., users' home computers) to contribute. The minimum space requirement to contribute should be approximately independent of the data size. Second, if a collection of nodes together receive rewards commensurate with contributing a total of m blocks of space, then we want the following reassurances: 1) if m is at least the database size, we should be able to reconstruct the entire dataset; and 2) these nodes should actually be committing roughly m space in aggregate - specifically, when m is much larger than the data size, these nodes cannot store only one copy of the database, and be able to impersonate arbitrarily many pseudonyms and get unbounded rewards. We propose new definitions that mathematically formalize the aforementioned requirements of an iDDA scheme. We also devise an efficient construction in the random oracle model which satisfies the desired security requirements. Our scheme incurs only Õ(1) audit cost, as well as Õ(1) update cost for both the publisher and each node, where Õ(⋅) hides polylogarithmic factors. Further, the minimum space provisioning required to contribute is as small as polylogarithmic. Our construction exposes several interesting technical challenges. Specifically, we show that a straightforward application of the standard hierarchical data structure fails, since both our security definition and the underlying cryptographic primitives we employ lack the desired compositional guarantees. We devise novel techniques to overcome these compositional issues, resulting in a construction with provable security while still retaining efficiency. Finally, our new definitions also make a conceptual contribution, and lay the theoretical groundwork for the study of iDDA. We raise several interesting open problems along this direction.
Cite as

Elaine Shi, Rose Silver, and Changrui Mu. Decentralized Data Archival: New Definitions and Constructions. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 116:1-116:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{shi_et_al:LIPIcs.ITCS.2026.116,
  author =	{Shi, Elaine and Silver, Rose and Mu, Changrui},
  title =	{{Decentralized Data Archival: New Definitions and Constructions}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{116:1--116:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.116},
  URN =		{urn:nbn:de:0030-drops-254037},
  doi =		{10.4230/LIPIcs.ITCS.2026.116},
  annote =	{Keywords: Decentralized Data Archival}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.89
A Simple Algorithm for Trimmed Multipoint Evaluation

Authors: Nick Fischer, Melvin Kallmayer, and Leo Wennmann

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
Evaluating a polynomial on a set of points is a fundamental task in computer algebra. In this work, we revisit a particular variant called trimmed multipoint evaluation: given an n-variate polynomial with bounded individual degree d and total degree D, the goal is to evaluate it on a natural class of input points. This problem arises as a key subroutine in recent algorithmic results [Dinur; SODA '21], [Dell, Haak, Kallmayer, Wennmann; SODA '25]. It is known that trimmed multipoint evaluation can be solved in near-linear time [van der Hoeven, Schost; AAECC '13] by a clever yet somewhat involved algorithm. We give a simple recursive algorithm that avoids heavy computer-algebraic machinery, and can be readily understood by researchers without specialized background.
Cite as

Nick Fischer, Melvin Kallmayer, and Leo Wennmann. A Simple Algorithm for Trimmed Multipoint Evaluation. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 89:1-89:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{fischer_et_al:LIPIcs.ESA.2025.89,
  author =	{Fischer, Nick and Kallmayer, Melvin and Wennmann, Leo},
  title =	{{A Simple Algorithm for Trimmed Multipoint Evaluation}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{89:1--89:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.89},
  URN =		{urn:nbn:de:0030-drops-245574},
  doi =		{10.4230/LIPIcs.ESA.2025.89},
  annote =	{Keywords: Algebraic Algorithms, Multipoint Evaluation, Interpolation, LU Decomposition}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.38
Low-Degree Polynomials Are Good Extractors

Authors: Omar Alrabiah, Jesse Goodman, Jonathan Mosheiff, and João Ribeiro

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
We prove that random low-degree polynomials (over 𝔽₂) are unbiased, in an extremely general sense. That is, we show that random low-degree polynomials are good randomness extractors for a wide class of distributions. Prior to our work, such results were only known for the small families of (1) uniform sources, (2) affine sources, and (3) local sources. We significantly generalize these results, and prove the following. 1) Low-degree polynomials extract from small families. We show that a random low-degree polynomial is a good low-error extractor for any small family of sources. In particular, we improve the positive result of Alrabiah, Chattopadhyay, Goodman, Li, and Ribeiro (ICALP 2022) for local sources, and give new results for polynomial and variety sources via a single unified approach. 2) Low-degree polynomials extract from sumset sources. We show that a random low-degree polynomial is a good extractor for sumset sources, which are the most general large family of sources (capturing independent sources, interleaved sources, small-space sources, and more). Formally, for any even d, we show that a random degree d polynomial is an ε-error extractor for n-bit sumset sources with min-entropy k = O(d(n/ε²)^{2/d}). This is nearly tight in the polynomial error regime. Our results on sumset extractors imply new complexity separations for linear ROBPs, and the tools that go into its proof may be of independent interest. The two main tools we use are a new structural result on sumset-punctured Reed-Muller codes, paired with a novel type of reduction between extractors. Using the new structural result, we obtain new limits on the power of sumset extractors, strengthening and generalizing the impossibility results of Chattopadhyay, Goodman, and Gurumukhani (ITCS 2024).
Cite as

Omar Alrabiah, Jesse Goodman, Jonathan Mosheiff, and João Ribeiro. Low-Degree Polynomials Are Good Extractors. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 38:1-38:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{alrabiah_et_al:LIPIcs.APPROX/RANDOM.2025.38,
  author =	{Alrabiah, Omar and Goodman, Jesse and Mosheiff, Jonathan and Ribeiro, Jo\~{a}o},
  title =	{{Low-Degree Polynomials Are Good Extractors}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{38:1--38:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.38},
  URN =		{urn:nbn:de:0030-drops-244048},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.38},
  annote =	{Keywords: randomness extractors, low-degree polynomials, local sources, polynomial sources, variety sources, sumset sources, sumset extractors, Reed-Muller codes, lower bounds}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.43
Gabidulin Codes Achieve List Decoding Capacity with an Order-Optimal Column-To-Row Ratio

Authors: Zeyu Guo, Chaoping Xing, Chen Yuan, and Zihan Zhang

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
In this paper, we show that random Gabidulin codes of block length n and rate R achieve the (average-radius) list decoding capacity of radius 1-R-ε in the rank metric with an order-optimal column-to-row ratio of O(ε). This extends the recent work of Guo, Xing, Yuan, and Zhang (FOCS 2024), improving their column-to-row ratio from O(ε/n) to O(ε). For completeness, we also establish a matching lower bound on the column-to-row ratio for capacity-achieving Gabidulin codes in the rank metric. Our proof techniques build on the work of Guo and Zhang (FOCS 2023), who showed that randomly punctured Reed-Solomon codes over fields of quadratic size attain the generalized Singleton bound of Shangguan and Tamo (STOC 2020) in the Hamming metric. The proof of our lower bound follows the method of Alrabiah, Guruswami, and Li (SODA 2024) for codes in the Hamming metric.
Cite as

Zeyu Guo, Chaoping Xing, Chen Yuan, and Zihan Zhang. Gabidulin Codes Achieve List Decoding Capacity with an Order-Optimal Column-To-Row Ratio. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 43:1-43:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{guo_et_al:LIPIcs.APPROX/RANDOM.2025.43,
  author =	{Guo, Zeyu and Xing, Chaoping and Yuan, Chen and Zhang, Zihan},
  title =	{{Gabidulin Codes Achieve List Decoding Capacity with an Order-Optimal Column-To-Row Ratio}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{43:1--43:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.43},
  URN =		{urn:nbn:de:0030-drops-244095},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.43},
  annote =	{Keywords: coding theory, error-correcting codes, Gabidulin codes, rank-metric codes}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.57
List-Recovery of Random Linear Codes over Small Fields

Authors: Dean Doron, Jonathan Mosheiff, Nicolas Resch, and João Ribeiro

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
We study list-recoverability of random linear codes over small fields, both from errors and from erasures. We consider codes of rate ε-close to capacity, and aim to bound the dependence of the output list size L on ε, the input list size 𝓁, and the alphabet size q. Prior to our work, the best upper bound was L = q^O(𝓁/ε) (Zyablov and Pinsker, Prob. Per. Inf. 1981). Previous work has identified cases in which linear codes provably perform worse than non-linear codes with respect to list-recovery. While there exist non-linear codes that achieve L = O(𝓁/ε), we know that L ≥ 𝓁^Ω(1/ε) is necessary for list recovery from erasures over fields of small characteristic, and for list recovery from errors over large alphabets. We show that in other relevant regimes there is no significant price to pay for linearity, in the sense that we get the correct dependence on the gap-to-capacity ε and go beyond the Zyablov-Pinsker bound for the first time. Specifically, when q is constant and ε approaches zero, - For list-recovery from erasures over prime fields, we show that L ≤ C₁/ε. By prior work, such a result cannot be obtained for low-characteristic fields. - For list-recovery from errors over arbitrary fields, we prove that L ≤ C₂/ε. Above, C₁ and C₂ depend on the decoding radius, input list size, and field size. We provide concrete bounds on the constants above, and the upper bounds on L improve upon the Zyablov-Pinsker bound whenever q ≤ 2^{(1/ε)^c} for some small universal constant c > 0.
Cite as

Dean Doron, Jonathan Mosheiff, Nicolas Resch, and João Ribeiro. List-Recovery of Random Linear Codes over Small Fields. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 57:1-57:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{doron_et_al:LIPIcs.APPROX/RANDOM.2025.57,
  author =	{Doron, Dean and Mosheiff, Jonathan and Resch, Nicolas and Ribeiro, Jo\~{a}o},
  title =	{{List-Recovery of Random Linear Codes over Small Fields}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{57:1--57:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.57},
  URN =		{urn:nbn:de:0030-drops-244239},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.57},
  annote =	{Keywords: List recovery, random linear codes}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.53
Near-Optimal List-Recovery of Linear Code Families

Authors: Ray Li and Nikhil Shagrithaya

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
We prove several results on linear codes achieving list-recovery capacity. We show that random linear codes achieve list-recovery capacity with constant output list size (independent of the alphabet size and length). That is, over alphabets of size at least 𝓁^Ω(1/ε), random linear codes of rate R are (1-R-ε, 𝓁, (𝓁/ε)^O(𝓁/ε))-list-recoverable for all R ∈ (0,1) and 𝓁. Together with a result of Levi, Mosheiff, and Shagrithaya, this implies that randomly punctured Reed-Solomon codes also achieve list-recovery capacity. We also prove that our output list size is near-optimal among all linear codes: all (1-R-ε, 𝓁, L)-list-recoverable linear codes must have L ≥ 𝓁^{Ω(R/ε)}. Our simple upper bound combines the Zyablov-Pinsker argument with recent bounds from Kopparty, Ron-Zewi, Saraf, Wootters, and Tamo on the maximum intersection of a "list-recovery ball" and a low-dimensional subspace with large distance. Our lower bound is inspired by a recent lower bound of Chen and Zhang.
Cite as

Ray Li and Nikhil Shagrithaya. Near-Optimal List-Recovery of Linear Code Families. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 53:1-53:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{li_et_al:LIPIcs.APPROX/RANDOM.2025.53,
  author =	{Li, Ray and Shagrithaya, Nikhil},
  title =	{{Near-Optimal List-Recovery of Linear Code Families}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{53:1--53:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.53},
  URN =		{urn:nbn:de:0030-drops-244199},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.53},
  annote =	{Keywords: Error-Correcting Codes, Randomness, List-Recovery, Reed-Solomon Codes, Random Linear Codes}
}
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
DOI: 10.4230/LIPIcs.CCC.2025.15
Algebraic Pseudorandomness in VNC⁰

Authors: Robert Andrews

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

Abstract
We study the arithmetic complexity of hitting set generators, which are pseudorandom objects used for derandomization of the polynomial identity testing problem. We give new explicit constructions of hitting set generators whose outputs are computable in VNC⁰, i.e., can be computed by arithmetic formulas of constant size. Unconditionally, we construct a VNC⁰-computable generator that hits arithmetic circuits of constant depth and polynomial size. We also give conditional constructions, under strong but plausible hardness assumptions, of VNC⁰-computable generators that hit arithmetic formulas and arithmetic branching programs of polynomial size, respectively. As a corollary of our constructions, we derive lower bounds for subsystems of the Geometric Ideal Proof System of Grochow and Pitassi. Constructions of such generators are implicit in prior work of Kayal on lower bounds for the degree of annihilating polynomials. Our main contribution is a construction whose correctness relies on circuit complexity lower bounds rather than degree lower bounds.
Cite as

Robert Andrews. Algebraic Pseudorandomness in VNC⁰. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 15:1-15:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{andrews:LIPIcs.CCC.2025.15,
  author =	{Andrews, Robert},
  title =	{{Algebraic Pseudorandomness in VNC⁰}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{15:1--15:15},
  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.2025.15},
  URN =		{urn:nbn:de:0030-drops-237092},
  doi =		{10.4230/LIPIcs.CCC.2025.15},
  annote =	{Keywords: Polynomial identity testing, Algebraic circuits, Ideal Proof System}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.28
Faster & Deterministic FPT Algorithm for Worst-Case Tensor Decomposition

Authors: Vishwas Bhargava and Devansh Shringi

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We present a deterministic 2^{k^{𝒪(1)}} poly(n,d) time algorithm for decomposing d-dimensional, width-n tensors of rank at most k over ℝ and ℂ. This improves upon the previous randomized algorithm of Peleg, Shpilka, and Volk (ITCS '24) that takes 2^{k^{k^{𝒪(k)}}} poly(n,d) time and the deterministic n^k^k time algorithms of Bhargava, Saraf, and Volkovich (STOC '21). Our work resolves an open question asked by Peleg, Shpilka, and Volk (ITCS '24) on whether a deterministic Fixed Parameter Tractable (FPT) algorithm exists for worst-case tensor decomposition. We also make substantial progress on the fundamental problem of how the tractability of tensor decomposition varies as the tensor rank increases. Our result implies that we can achieve deterministic polynomial-time decomposition as long as the rank of the tensor is at most (log n)^{1/C}, where C is some fixed constant independent of n and d. Further, we note that there cannot exist a polynomial-time algorithm for k = ω(log n) unless ETH fails. Our algorithm works for all fields; however, the time complexity worsens to 2^{k^{k^{𝒪(1)}}} and requires randomization for finite fields of large characteristics. Both conditions are provably necessary unless there are improvements in the state of the art for system solving over the corresponding fields. Our approach achieves this by designing a proper learning (reconstruction) algorithm for set-multilinear depth-3 arithmetic circuits. On a technical note, we design a "partial" clustering algorithm for set-multilinear depth-3 arithmetic circuits that lets us isolate a cluster from any set-multilinear depth-3 circuit while preserving the structure of the circuit.
Cite as

Vishwas Bhargava and Devansh Shringi. Faster & Deterministic FPT Algorithm for Worst-Case Tensor Decomposition. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 28:1-28:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{bhargava_et_al:LIPIcs.ICALP.2025.28,
  author =	{Bhargava, Vishwas and Shringi, Devansh},
  title =	{{Faster \& Deterministic FPT Algorithm for Worst-Case Tensor Decomposition}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{28:1--28:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.28},
  URN =		{urn:nbn:de:0030-drops-234052},
  doi =		{10.4230/LIPIcs.ICALP.2025.28},
  annote =	{Keywords: Algebraic circuits, Deterministic algorithms, FPT algorithm, Learning circuits, Reconstruction, Tensor Decomposition, Tensor Rank}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.60
Random Reed-Solomon Codes Achieve the Half-Singleton Bound for Insertions and Deletions over Linear-Sized Alphabets

Authors: Roni Con, Zeyu Guo, Ray Li, and Zihan Zhang

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
In this paper, we prove that with high probability, random Reed-Solomon codes approach the half-Singleton bound - the optimal rate versus error tradeoff for linear insdel codes - with linear-sized alphabets. More precisely, we prove that, for any ε > 0 and positive integers n and k, with high probability, random Reed-Solomon codes of length n and dimension k can correct (1-ε)n-2k+1 adversarial insdel errors over alphabets of size n+2^{poly(1/ε)}k. This significantly improves upon the alphabet size demonstrated in the work of Con, Shpilka, and Tamo (IEEE TIT, 2023), who showed the existence of Reed-Solomon codes with exponential alphabet size Õ(binom(n,2k-1)²) precisely achieving the half-Singleton bound. Our methods are inspired by recent works on list-decoding Reed-Solomon codes. Brakensiek-Gopi-Makam (STOC 2023) showed that random Reed-Solomon codes are list-decodable up to capacity with exponential-sized alphabets, and Guo-Zhang (FOCS 2023) and Alrabiah-Guruswami-Li (STOC 2024) improved the alphabet-size to linear. We achieve a similar alphabet-size reduction by similarly establishing strong bounds on the probability that certain random rectangular matrices are full rank. To accomplish this in our insdel context, our proof combines the random matrix techniques from list-decoding with structural properties of Longest Common Subsequences.
Cite as

Roni Con, Zeyu Guo, Ray Li, and Zihan Zhang. Random Reed-Solomon Codes Achieve the Half-Singleton Bound for Insertions and Deletions over Linear-Sized Alphabets. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 60:1-60:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{con_et_al:LIPIcs.ICALP.2025.60,
  author =	{Con, Roni and Guo, Zeyu and Li, Ray and Zhang, Zihan},
  title =	{{Random Reed-Solomon Codes Achieve the Half-Singleton Bound for Insertions and Deletions over Linear-Sized Alphabets}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{60:1--60:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.60},
  URN =		{urn:nbn:de:0030-drops-234372},
  doi =		{10.4230/LIPIcs.ICALP.2025.60},
  annote =	{Keywords: coding theory, error-correcting codes, Reed-Solomon codes, insdel, insertion-deletion errors, half-Singleton bound}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.13
Quantum Speedup for Sampling Random Spanning Trees

Authors: Simon Apers, Minbo Gao, Zhengfeng Ji, and Chenghua Liu

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We present a quantum algorithm for sampling random spanning trees from a weighted graph in Õ(√{mn}) time, where n and m denote the number of vertices and edges, respectively. Our algorithm has sublinear runtime for dense graphs and achieves a quantum speedup over the best-known classical algorithm, which runs in Õ(m) time. The approach carefully combines, on one hand, a classical method based on "large-step" random walks for reduced mixing time and, on the other hand, quantum algorithmic techniques, including quantum graph sparsification and a sampling-without-replacement variant of Hamoudi’s multiple-state preparation. We also establish a matching lower bound, proving the optimality of our algorithm up to polylogarithmic factors. These results highlight the potential of quantum computing in accelerating fundamental graph sampling problems.
Cite as

Simon Apers, Minbo Gao, Zhengfeng Ji, and Chenghua Liu. Quantum Speedup for Sampling Random Spanning Trees. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 13:1-13:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{apers_et_al:LIPIcs.ICALP.2025.13,
  author =	{Apers, Simon and Gao, Minbo and Ji, Zhengfeng and Liu, Chenghua},
  title =	{{Quantum Speedup for Sampling Random Spanning Trees}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{13:1--13:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.13},
  URN =		{urn:nbn:de:0030-drops-233907},
  doi =		{10.4230/LIPIcs.ICALP.2025.13},
  annote =	{Keywords: Quantum Computing, Quantum Algorithms, Random Spanning Trees}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2025.35
Chain of Grounded Objectives: Concise Goal-Oriented Prompting for Code Generation

Authors: Sangyeop Yeo, Seung-Won Hwang, and Yu-Seung Ma

Published in: LIPIcs, Volume 333, 39th European Conference on Object-Oriented Programming (ECOOP 2025)

Abstract
The use of Large Language Models (LLMs) for code generation has gained significant attention in recent years. Existing methods often aim to improve the quality of generated code by incorporating additional contextual information or guidance into input prompts. Many of these approaches adopt process-oriented reasoning strategies, mimicking human-like step-by-step thinking; however, they may not always align with the structured nature of programming languages. This paper introduces Chain of Grounded Objectives (CGO), a concise goal-oriented prompting approach that embeds functional objectives into prompts to enhance code generation. By focusing on precisely defined objectives rather than explicit procedural steps, CGO aligns more naturally with programming tasks while retaining flexibility. Empirical evaluations on HumanEval, MBPP, their extended versions, and LiveCodeBench show that CGO achieves accuracy comparable to or better than existing methods while using fewer tokens, making it a more efficient approach to LLM-based code generation.
Cite as

Sangyeop Yeo, Seung-Won Hwang, and Yu-Seung Ma. Chain of Grounded Objectives: Concise Goal-Oriented Prompting for Code Generation. In 39th European Conference on Object-Oriented Programming (ECOOP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 333, pp. 35:1-35:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{yeo_et_al:LIPIcs.ECOOP.2025.35,
  author =	{Yeo, Sangyeop and Hwang, Seung-Won and Ma, Yu-Seung},
  title =	{{Chain of Grounded Objectives: Concise Goal-Oriented Prompting for Code Generation}},
  booktitle =	{39th European Conference on Object-Oriented Programming (ECOOP 2025)},
  pages =	{35:1--35:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-373-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{333},
  editor =	{Aldrich, Jonathan and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2025.35},
  URN =		{urn:nbn:de:0030-drops-233271},
  doi =		{10.4230/LIPIcs.ECOOP.2025.35},
  annote =	{Keywords: Artificial Intelligence, Natural Language Processing, Prompt Design, Large Language Models, Code Generation}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.52
Uniform Bounds on Product Sylvester-Gallai Configurations

Authors: Abhibhav Garg, Rafael Oliveira, and Akash Kumar Sengupta

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
In this work, we explore a non-linear extension of the classical Sylvester-Gallai configuration. Let 𝕂 be an algebraically closed field of characteristic zero, and let ℱ = {F_1, …, F_m} ⊂ 𝕂[x_1, …, x_N] denote a collection of irreducible homogeneous polynomials of degree at most d, where each F_i is not a scalar multiple of any other F_j for i ≠ j. We define ℱ to be a product Sylvester-Gallai configuration if, for any two distinct polynomials F_i, F_j ∈ ℱ, the following condition is satisfied: ∏_{k≠i, j} F_k ∈ rad (F_i, F_j) . We prove that product Sylvester-Gallai configurations are inherently low dimensional. Specifically, we show that there exists a function λ : ℕ → ℕ, independent of 𝕂, N, and m, such that any product Sylvester-Gallai configuration must satisfy: dim(span_𝕂(ℱ)) ≤ λ(d). This result generalizes the main theorems from (Shpilka 2019, Peleg and Shpilka 2020, Oliveira and Sengupta 2023), and gets us one step closer to a full derandomization of the polynomial identity testing problem for the class of depth 4 circuits with bounded top and bottom fan-in.
Cite as

Abhibhav Garg, Rafael Oliveira, and Akash Kumar Sengupta. Uniform Bounds on Product Sylvester-Gallai Configurations. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 52:1-52:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{garg_et_al:LIPIcs.SoCG.2025.52,
  author =	{Garg, Abhibhav and Oliveira, Rafael and Sengupta, Akash Kumar},
  title =	{{Uniform Bounds on Product Sylvester-Gallai Configurations}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{52:1--52:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.52},
  URN =		{urn:nbn:de:0030-drops-232043},
  doi =		{10.4230/LIPIcs.SoCG.2025.52},
  annote =	{Keywords: Sylvester-Gallai theorem, arrangements of hypersurfaces, algebraic complexity, polynomial identity testing, algebraic geometry, commutative algebra}
}
  • Refine by Type
  • 25 Document/PDF
  • 16 Document/HTML

  • Refine by Publication Year
  • 3 2026
  • 14 2025
  • 2 2024
  • 1 2021
  • 3 2020
  • Show More...

  • Refine by Author
  • 10 Guo, Zeyu
  • 2 Andrews, Robert
  • 2 Li, Ray
  • 2 Mosheiff, Jonathan
  • 2 Ribeiro, João
  • Show More...

  • Refine by Series/Journal
  • 25 LIPIcs

  • Refine by Classification
  • 9 Theory of computation → Algebraic complexity theory
  • 9 Theory of computation → Pseudorandomness and derandomization
  • 6 Mathematics of computing → Coding theory
  • 3 Theory of computation → Error-correcting codes
  • 2 Mathematics of computing → Computations in finite fields
  • Show More...

  • Refine by Keyword
  • 3 error-correcting codes
  • 3 polynomial identity testing
  • 2 Algebraic circuits
  • 2 Error-Correcting Codes
  • 2 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