37 Search Results for "Hatami, Pooya"

Document
DOI: 10.4230/LIPIcs.CCC.2026.31
Optimal Testing of Reed-Muller Codes with an Online Adversary

Authors: Esty Kelman, Uri Meir, and Kai Zhe Zheng

Published in: LIPIcs, Volume 383, 41st Computational Complexity Conference (CCC 2026)

Abstract
Motivated by applications to property testing in the online-erasure model of Kalemaj, Raskhodnikova, and Varma (ITCS 2022 and Theory of Computing 2023), we define and analyze semi-sample-based testers for Reed-Muller codes. The task in Reed-Muller testing is to determine whether an input function f: 𝔽ⁿ → 𝔽 belongs to the Reed-Muller code or is far from it, using as few point queries to f as possible. Reed-Muller testing is a well-studied task with its roots in both the Property Testing and Probabilistically Checkable Proofs literature. The online-erasure model introduces a twist: after each query made, an adversary may erase up to t points of the input function, potentially thwarting any test in which the queries follow a predictable pattern. Semi-sample-based testers are a hybrid between sample-based testers - which can only make uniformly random queries to the input function - and standard testers, which can choose their queries freely. They are designed with the online-erasure model in mind and operate by first choosing some subset S of the domain and then making their queries uniformly at random inside of S. We describe semi-sample-based testers for the Reed-Muller code and give an optimal analysis of their soundness. Consequently, we show that semi-sample-based testers are indeed effective in the presence of online erasures, and thereby achieve optimal query complexity for testing the Reed-Muller code in the online-erasure model. This result improves upon prior work of Minzer and Zheng (SODA 2024). As an added bonus, we show that semi-sample-based testers also exist for the lifted affine-invariant codes of Guo, Kopparty, and Sudan (ITCS 2013), thereby providing the first known testers for these codes in the online-erasure model.
Cite as

Esty Kelman, Uri Meir, and Kai Zhe Zheng. Optimal Testing of Reed-Muller Codes with an Online Adversary. In 41st Computational Complexity Conference (CCC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 383, pp. 31:1-31:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kelman_et_al:LIPIcs.CCC.2026.31,
  author =	{Kelman, Esty and Meir, Uri and Zheng, Kai Zhe},
  title =	{{Optimal Testing of Reed-Muller Codes with an Online Adversary}},
  booktitle =	{41st Computational Complexity Conference (CCC 2026)},
  pages =	{31:1--31:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-437-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{383},
  editor =	{Moshkovitz, Dana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2026.31},
  URN =		{urn:nbn:de:0030-drops-270732},
  doi =		{10.4230/LIPIcs.CCC.2026.31},
  annote =	{Keywords: Property testing, Low degree testing}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.30
Spectral Norm, Economical Sieve, and Linear Invariance Testing of Boolean Functions

Authors: Swarnalipa Datta, Arijit Ghosh, Chandrima Kayal, Manaswi Paraashar, and Manmatha Roy

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
Given Boolean functions f, g : 𝔽₂ⁿ → {-1,+1}, we say they are linearly isomorphic if there exists A ∈ GL_n(𝔽₂) such that f(x) = g(Ax) for all x. We study this problem in the tolerant property testing framework under the known-unknown model, where g is given explicitly and f is accessible only via oracle queries, meaning the algorithm may adaptively request the value of f(x) for inputs x ∈ 𝔽₂ⁿ of its choice. Given parameters ε ≥ 0 and ω > 0, the goal is to distinguish whether there exists A ∈ GL_n(𝔽₂) such that the normalized Hamming distance between f and g(Ax) is at most ε, or whether for every A ∈ GL_n(𝔽₂) the distance is at least ε+ω. Our main result is a tolerant tester making Õ ((m/ω) ⁴) queries to f, where m is an upper bound on the spectral norm of g, improving the previous Õ ((m/ω) ^{24}) bound of Wimmer and Yoshida. We complement this with a nearly matching lower bound of Ω(m²) for constant ω (for example, ω = 1/4), improving the prior Ω(log m) lower bound of Grigorescu, Wimmer and Xie. A key technical ingredient on the algorithmic side is a query-efficient local list corrector. For the lower bound, we give a reduction from communication complexity using a novel subclass of Maiorana-McFarland functions from symmetric-key cryptography.
Cite as

Swarnalipa Datta, Arijit Ghosh, Chandrima Kayal, Manaswi Paraashar, and Manmatha Roy. Spectral Norm, Economical Sieve, and Linear Invariance Testing of Boolean Functions. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 30:1-30:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{datta_et_al:LIPIcs.STACS.2026.30,
  author =	{Datta, Swarnalipa and Ghosh, Arijit and Kayal, Chandrima and Paraashar, Manaswi and Roy, Manmatha},
  title =	{{Spectral Norm, Economical Sieve, and Linear Invariance Testing of Boolean Functions}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{30:1--30:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.30},
  URN =		{urn:nbn:de:0030-drops-255194},
  doi =		{10.4230/LIPIcs.STACS.2026.30},
  annote =	{Keywords: Boolean Function, Isomorphism of Boolean Function, Fourier Analysis, Sublinear Algorithm, Property Testing}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.22
Simplicial Covering Dimension of Extremal Concept Classes

Authors: Ari Blondal, Hamed Hatami, Pooya Hatami, Chavdar Lalov, and Sivan Tretiak

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

Abstract
Dimension theory is a branch of topology concerned with defining and analyzing dimensions of geometric and topological spaces in purely topological terms. In this work, we adapt the classical notion of topological dimension (Lebesgue covering) to binary concept classes. The topological space naturally associated with a concept class is its space of realizable distributions. The loss function and the class itself induce a simplicial structure on this space, with respect to which we define a simplicial covering dimension. We prove that for finite concept classes, this simplicial covering dimension exactly characterizes the list replicability number (equivalently, global stability) in PAC learning. This connection allows us to apply tools from classical dimension theory to compute the exact list replicability number of the broad family of extremal concept classes.
Cite as

Ari Blondal, Hamed Hatami, Pooya Hatami, Chavdar Lalov, and Sivan Tretiak. Simplicial Covering Dimension of Extremal Concept Classes. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 22:1-22:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{blondal_et_al:LIPIcs.ITCS.2026.22,
  author =	{Blondal, Ari and Hatami, Hamed and Hatami, Pooya and Lalov, Chavdar and Tretiak, Sivan},
  title =	{{Simplicial Covering Dimension of Extremal Concept Classes}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{22:1--22:24},
  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.2026.22},
  URN =		{urn:nbn:de:0030-drops-253094},
  doi =		{10.4230/LIPIcs.ITCS.2026.22},
  annote =	{Keywords: PAC Learning, Extremal Concept Classes, Replicability, List Replicability, Topology, Geometry}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.70
Unconditional Pseudorandomness Against Shallow Quantum Circuits

Authors: Soumik Ghosh, Sathyawageeswar Subramanian, and Wei Zhan

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

Abstract
Quantum computational pseudorandomness has emerged as a fundamental notion that spans connections to complexity theory, cryptography and fundamental physics. However, all known constructions of efficient quantum-secure pseudorandom objects rely on complexity theoretic assumptions. In this work, we establish the first unconditionally secure efficient pseudorandom constructions against shallow-depth quantum circuit classes. We prove that: - Any quantum state 2-design yields unconditional pseudorandomness against both QNC⁰ circuits with arbitrarily many ancillae and AC⁰∘QNC⁰ circuits with nearly linear ancillae. - Random phased subspace states, where the phases are picked using a 4-wise independent function, are unconditionally pseudoentangled against the above circuit classes. - Any unitary 2-design yields unconditionally secure parallel-query pseudorandom unitaries against geometrically local QNC⁰ adversaries, even with limited AC⁰ postprocessing. Our results stand in stark contrast to the standard guarantee of the 2-design property, which only ensures that they cannot be distinguished from Haar random ensembles using two copies or queries. Our work demonstrates that quantum computational pseudorandomness can be achieved unconditionally for natural classes of restricted adversaries, opening new directions in quantum complexity theory.
Cite as

Soumik Ghosh, Sathyawageeswar Subramanian, and Wei Zhan. Unconditional Pseudorandomness Against Shallow Quantum Circuits. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 70:1-70:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ghosh_et_al:LIPIcs.ITCS.2026.70,
  author =	{Ghosh, Soumik and Subramanian, Sathyawageeswar and Zhan, Wei},
  title =	{{Unconditional Pseudorandomness Against Shallow Quantum Circuits}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{70:1--70:25},
  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.2026.70},
  URN =		{urn:nbn:de:0030-drops-253578},
  doi =		{10.4230/LIPIcs.ITCS.2026.70},
  annote =	{Keywords: quantum pseudorandomness, shallow quantum circuits, pseudorandomness, t-designs}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.34
Testing Classical Properties from Quantum Data

Authors: Matthias C. Caro, Preksha Naik, and Joseph Slote

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

Abstract
Many properties of Boolean functions can be tested far more efficiently than the function itself can be learned. However, this dramatic advantage often disappears when testers are limited to random samples of f instead of adaptively chosen queries to f. In this work we investigate the quantum version of this restriction: quantum algorithms that test properties of a Boolean function f solely from copies of either the function state |f⟩∝ ∑_x|x,f(x)⟩ or the phase state |(-1)^f⟩∝ ∑_x (-1)^{f(x)}|x⟩. Quantum advantage in testing from data. For monotonicity, symmetry, and triangle-freeness, we show passive quantum testers are unboundedly or super-polynomially better than their classical passive testing counterparts. They are competitive with classic query-based testers in each case. Inadequacy of Fourier sampling. Our new testers use techniques beyond quantum Fourier sampling, and it turns out this is necessary: we show a certain class of bent functions can be tested from 𝒪(1) function states but has a sample complexity lower bound of 2^{Ω(n)} for any tester relying exclusively on Fourier and classical samples. Classical queries vs. quantum data. Our passive quantum testers are competitive with classical query-based testers, but this isn't universal: we exhibit a testing problem that can be solved from 𝒪(1) classical queries but requires Ω(2^{n/2}) function state copies. The Forrelation problem provides a separation of the same magnitude in the opposite direction, so we conclude that quantum data and classical queries are "maximally incomparable" resources for testing. Towards lower bounds. We also begin the study of lower bounds for testing from quantum data. For quantum monotonicity testing, we prove that the ensembles of [Goldreich et al., 2000; Black, 2024], which give exponential lower bounds for classical sample-based testing, do not yield any nontrivial lower bounds for testing from quantum data. New insights specific to quantum data will be required for proving copy complexity lower bounds for testing in this model.
Cite as

Matthias C. Caro, Preksha Naik, and Joseph Slote. Testing Classical Properties from Quantum Data. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 34:1-34:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{caro_et_al:LIPIcs.ITCS.2026.34,
  author =	{Caro, Matthias C. and Naik, Preksha and Slote, Joseph},
  title =	{{Testing Classical Properties from Quantum Data}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{34:1--34:26},
  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.2026.34},
  URN =		{urn:nbn:de:0030-drops-253213},
  doi =		{10.4230/LIPIcs.ITCS.2026.34},
  annote =	{Keywords: Quantum Property Testing, Quantum Data, Boolean Functions}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.58
Equality Is Far Weaker Than Constant-Cost Communication

Authors: Mika Göös, Nathaniel Harms, and Artur Riazanov

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

Abstract
We exhibit an n-bit communication problem with a constant-cost randomized protocol but which requires n^Ω(1) deterministic (or even non-deterministic) queries to an Equality oracle. Therefore, even constant-cost randomized protocols cannot be efficiently "derandomized" using Equality oracles. This improves on several recent results and answers a question from the survey of Hatami and Hatami (SIGACT News 2024). It also gives a significantly simpler and quantitatively superior proof of the main result of Fang, Göös, Harms, and Hatami (STOC 2025), that constant-cost communication does not reduce to the k-Hamming Distance hierarchy.
Cite as

Mika Göös, Nathaniel Harms, and Artur Riazanov. Equality Is Far Weaker Than Constant-Cost Communication. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 58:1-58:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{goos_et_al:LIPIcs.APPROX/RANDOM.2025.58,
  author =	{G\"{o}\"{o}s, Mika and Harms, Nathaniel and Riazanov, Artur},
  title =	{{Equality Is Far Weaker Than Constant-Cost Communication}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{58:1--58:14},
  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.2025.58},
  URN =		{urn:nbn:de:0030-drops-244246},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.58},
  annote =	{Keywords: Equality oracle, constant-cost communication, gamma-2 norm, spectral norm}
}
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)

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@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.2025.35
Fooling Near-Maximal Decision Trees

Authors: William M. Hoza and Zelin Lv

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

Abstract
For any constant α > 0, we construct an explicit pseudorandom generator (PRG) that fools n-variate decision trees of size m with error ε and seed length (1 + α) ⋅ log₂ m + O(log(1/ε) + log log n). For context, one can achieve seed length (2 + o(1)) ⋅ log₂ m + O(log(1/ε) + log log n) using well-known constructions and analyses of small-bias distributions, but such a seed length is trivial when m ≥ 2^{n/2}. Our approach is to develop a new variant of the classic concept of almost k-wise independence, which might be of independent interest. We say that a distribution X over {0, 1}ⁿ is k-wise ε-probably uniform if every Boolean function f that depends on only k variables satisfies 𝔼[f(X)] ≥ (1 - ε) ⋅ 𝔼[f]. We show how to sample a k-wise ε-probably uniform distribution using a seed of length (1 + α) ⋅ k + O(log(1/ε) + log log n). Meanwhile, we also show how to construct a set H ⊆ 𝔽₂ⁿ such that every feasible system of k linear equations in n variables over 𝔽₂ has a solution in H. The cardinality of H and the time complexity of enumerating H are at most 2^{k + o(k) + polylog n}, whereas small-bias distributions would give a bound of 2^{2k + O(log(n/k))}. By combining our new constructions with work by Chen and Kabanets (TCS 2016), we obtain nontrivial PRGs and hitting sets for linear-size Boolean circuits. Specifically, we get an explicit PRG with seed length (1 - Ω(1)) ⋅ n that fools circuits of size 2.99 ⋅ n over the U₂ basis, and we get a hitting set with time complexity 2^{(1 - Ω(1)) ⋅ n} for circuits of size 2.49 ⋅ n over the B₂ basis.
Cite as

William M. Hoza and Zelin Lv. Fooling Near-Maximal Decision Trees. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 35:1-35:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hoza_et_al:LIPIcs.APPROX/RANDOM.2025.35,
  author =	{Hoza, William M. and Lv, Zelin},
  title =	{{Fooling Near-Maximal Decision Trees}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{35:1--35:24},
  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.2025.35},
  URN =		{urn:nbn:de:0030-drops-244019},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.35},
  annote =	{Keywords: almost k-wise independence, decision trees, pseudorandom generators}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.28
Implications of Better PRGs for Permutation Branching Programs

Authors: Dean Doron and William M. Hoza

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

Abstract
We study the challenge of derandomizing constant-width standard-order read-once branching programs (ROBPs). Let c ∈ [1, 2) be any constant. We prove that if there are explicit pseudorandom generators (PRGs) for width-6 length-n permutation ROBPs with error 1/n and seed length Õ(log^c n), then there are explicit hitting set generators (HSGs) for width-4 length-n ROBPs with threshold 1/polylog(n) and seed length Õ(log^c n). For context, there are known explicit PRGs that fool constant-width permutation ROBPs with error ε and seed length O(log(n)⋅log(1/ε)) (Koucký, Nimbhorkar, and Pudlák STOC 2011; De CCC 2011; Steinke ECCC 2012). When ε = 1/n, there are known constructions of weighted pseudorandom generators (WPRGs) that fool polynomial-width permutation ROBPs with seed length Õ(log^{3/2} n) (Pyne and Vadhan CCC 2021; Chen, Hoza, Lyu, Tal, and Wu FOCS 2023; Chattopadhyay and Liao ITCS 2024), but unweighted PRGs with seed length o(log² n) remain elusive. Meanwhile, for width-4 ROBPs, there are no known explicit PRGs, WPRGs, or HSGs with seed length o(log²n). Our reduction can be divided into two parts. First, we show that explicit low-error PRGs for width-6 permutation ROBPs with seed length Õ(log^c n) would imply explicit low-error PRGs for width-3 ROBPs with seed length Õ(log^c n). This would improve Meka, Reingold, and Tal’s PRG (STOC 2019), which has seed length o(log²n) only when the error parameter is relatively large. Second, we show that for any w, n, s, and ε, an explicit PRG for width-w ROBPs with error 0.01/n and seed length s would imply an explicit ε-HSG for width-(w + 1) ROBPs with seed length O(s + log(n)⋅log(1/ε)).
Cite as

Dean Doron and William M. Hoza. Implications of Better PRGs for Permutation Branching Programs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 28:1-28:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{doron_et_al:LIPIcs.APPROX/RANDOM.2025.28,
  author =	{Doron, Dean and Hoza, William M.},
  title =	{{Implications of Better PRGs for Permutation Branching Programs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{28:1--28:20},
  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.2025.28},
  URN =		{urn:nbn:de:0030-drops-243946},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.28},
  annote =	{Keywords: hitting set generators, pseudorandom generators, read-once branching programs}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.67
On Sums of INW Pseudorandom Generators

Authors: William M. Hoza and Zelin Lv

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

Abstract
We study a new approach for constructing pseudorandom generators (PRGs) that fool constant-width standard-order read-once branching programs (ROBPs). Let X be the n-bit output distribution of the INW PRG (Impagliazzo, Nisan, and Wigderson, STOC 1994), instantiated using expansion parameter λ. We prove that the bitwise XOR of t independent copies of X fools width-w programs with error n^{log(w + 1)} ⋅ (λ⋅log n)^t. Notably, this error bound is meaningful even for relatively large values of λ such as λ = 1/O(log n). Admittedly, our analysis does not yet imply any improvement in the bottom-line overall seed length required for fooling such programs - it just gives a new way of re-proving the well-known O(log² n) bound. Furthermore, we prove that this shortcoming is not an artifact of our analysis, but rather is an intrinsic limitation of our "XOR of INW" approach. That is, no matter how many copies of the INW generator we XOR together, and no matter how we set the expansion parameters, if the generator fools width-3 programs and the proof of correctness does not use any properties of the expander graphs except their spectral expansion, then we prove that the seed length of the generator is inevitably Ω(log² n). Still, we hope that our work might be a step toward constructing near-optimal PRGs fooling constant-width ROBPs. We suggest that one could try running the INW PRG on t correlated seeds, sampled via another PRG, and taking the bitwise XOR of the outputs.
Cite as

William M. Hoza and Zelin Lv. On Sums of INW Pseudorandom Generators. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 67:1-67:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hoza_et_al:LIPIcs.APPROX/RANDOM.2025.67,
  author =	{Hoza, William M. and Lv, Zelin},
  title =	{{On Sums of INW Pseudorandom Generators}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{67:1--67:24},
  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.2025.67},
  URN =		{urn:nbn:de:0030-drops-244330},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.67},
  annote =	{Keywords: INW generator, pseudorandomness, space-bounded computation, XOR Lemmas}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.66
Testing Isomorphism of Boolean Functions over Finite Abelian Groups

Authors: Swarnalipa Datta, Arijit Ghosh, Chandrima Kayal, Manaswi Paraashar, and Manmatha Roy

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

Abstract
Let f and g be Boolean functions over a finite Abelian group 𝒢, where g is fully known and f is accessible via queries; that is, given any x ∈ 𝒢, we can obtain the value f(x). We study the problem of tolerant isomorphism testing: given parameters ε ≥ 0 and τ > 0, the goal is to determine, using as few queries as possible, whether there exists an automorphism σ of 𝒢 such that the fractional Hamming distance between f∘σ and g is at most ε, or whether for every automorphism σ, the distance is at least ε + τ. We design an efficient tolerant property testing algorithm for this problem over finite Abelian groups with constant exponent. The exponent of a finite group refers to the largest order of any element in the group. The query complexity of our algorithm is polynomial in s and 1/τ, where s bounds the spectral norm of the function g, and τ is the tolerance parameter. In addition, we present an improved algorithm in the case where g is Fourier sparse, meaning that its Fourier expansion contains only a small number of nonzero coefficients. Our approach draws on key ideas from Abelian group theory and Fourier analysis, including the annihilator of a subgroup, Pontryagin duality, and a pseudo inner product defined over finite Abelian groups. We believe that these techniques will be useful more broadly in the design of property testing algorithms.
Cite as

Swarnalipa Datta, Arijit Ghosh, Chandrima Kayal, Manaswi Paraashar, and Manmatha Roy. Testing Isomorphism of Boolean Functions over Finite Abelian Groups. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 66:1-66:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{datta_et_al:LIPIcs.APPROX/RANDOM.2025.66,
  author =	{Datta, Swarnalipa and Ghosh, Arijit and Kayal, Chandrima and Paraashar, Manaswi and Roy, Manmatha},
  title =	{{Testing Isomorphism of Boolean Functions over Finite Abelian Groups}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{66:1--66:22},
  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.2025.66},
  URN =		{urn:nbn:de:0030-drops-244328},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.66},
  annote =	{Keywords: Analysis of Boolean functions, Abelian groups, Automorphism group, Function isomorphism, Spectral norm}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.49
Pseudorandomness of Expander Walks via Fourier Analysis on Groups

Authors: Fernando Granha Jeronimo, Tushant Mittal, and Sourya Roy

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

Abstract
A long line of work has studied the pseudorandomness properties of walks on expander graphs. A central goal is to measure how closely the distribution over n-length walks on an expander approximates the uniform distribution of n-independent elements. One approach to do so is to label the vertices of an expander with elements from an alphabet Σ, and study closeness of the mean of functions over Σⁿ, under these two distributions. We say expander walks ε-fool a function if the expander walk mean is ε-close to the true mean. There has been a sequence of works studying this question for various functions, such as the XOR function, the AND function, etc. We show that: - The class of symmetric functions is O(|Σ|λ)-fooled by expander walks over any generic λ-expander, and any alphabet Σ . This generalizes the result of Cohen, Peri, Ta-Shma [STOC'21] which analyzes it for |Σ| = 2, and exponentially improves the previous bound of O(|Σ|^O(|Σ|) λ), by Golowich and Vadhan [CCC'22]. Moreover, if the expander is a Cayley graph over ℤ_|Σ|, we get a further improved bound of O(√{|Σ|} λ). Morever, when Σ is a finite group G, we show the following for functions over Gⁿ: - The class of symmetric class functions is O({√|G|}/D λ}-fooled by expander walks over "structured" λ-expanders, if G is D-quasirandom. - We show a lower bound of Ω(λ) for symmetric functions for any finite group G (even for "structured" λ-expanders). - We study the Fourier spectrum of a class of non-symmetric functions arising from word maps, and show that they are exponentially fooled by expander walks. Our proof employs Fourier analysis over general groups, which contrasts with earlier works that have studied either the case of ℤ₂ or ℤ. This enables us to get quantitatively better bounds even for unstructured sets.
Cite as

Fernando Granha Jeronimo, Tushant Mittal, and Sourya Roy. Pseudorandomness of Expander Walks via Fourier Analysis on Groups. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 49:1-49:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jeronimo_et_al:LIPIcs.APPROX/RANDOM.2025.49,
  author =	{Jeronimo, Fernando Granha and Mittal, Tushant and Roy, Sourya},
  title =	{{Pseudorandomness of Expander Walks via Fourier Analysis on Groups}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{49:1--49:22},
  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.2025.49},
  URN =		{urn:nbn:de:0030-drops-244157},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.49},
  annote =	{Keywords: Expander graphs, pseudorandomness}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.29
Generalised Linial-Nisan Conjecture Is False for DNFs

Authors: Yaroslav Alekseev, Mika Göös, Ziyi Guan, Gilbert Maystre, Artur Riazanov, Dmitry Sokolov, and Weiqiang Yuan

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

Abstract
Aaronson (STOC 2010) conjectured that almost k-wise independence fools constant-depth circuits; he called this the generalised Linial-Nisan conjecture. Aaronson himself later found a counterexample for depth-3 circuits. We give here an improved counterexample for depth-2 circuits (DNFs). This shows, for instance, that Bazzi’s celebrated result (k-wise independence fools DNFs) cannot be generalised in a natural way. We also propose a way to circumvent our counterexample: We define a new notion of pseudorandomness called local couplings and show that it fools DNFs and even decision lists.
Cite as

Yaroslav Alekseev, Mika Göös, Ziyi Guan, Gilbert Maystre, Artur Riazanov, Dmitry Sokolov, and Weiqiang Yuan. Generalised Linial-Nisan Conjecture Is False for DNFs. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 29:1-29:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{alekseev_et_al:LIPIcs.CCC.2025.29,
  author =	{Alekseev, Yaroslav and G\"{o}\"{o}s, Mika and Guan, Ziyi and Maystre, Gilbert and Riazanov, Artur and Sokolov, Dmitry and Yuan, Weiqiang},
  title =	{{Generalised Linial-Nisan Conjecture Is False for DNFs}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{29:1--29:13},
  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.2025.29},
  URN =		{urn:nbn:de:0030-drops-237231},
  doi =		{10.4230/LIPIcs.CCC.2025.29},
  annote =	{Keywords: pseudorandomness, DNFs, bounded independence}
}
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)

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@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.2025.9
Pseudorandom Bits for Non-Commutative Programs

Authors: Chin Ho Lee and Emanuele Viola

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

Abstract
We obtain new explicit pseudorandom generators for several computational models involving groups. Our main results are as follows: 1) We consider read-once group-products over a finite group G, i.e., tests of the form ∏_{i=1}^n (g_i)^{x_i} where g_i ∈ G, a special case of read-once permutation branching programs. We give generators with optimal seed length c_G log(n/ε) over any p-group. The proof uses the small-bias plus noise paradigm, but derandomizes the noise to avoid the recursion in previous work. Our generator works when the bits are read in any order. Previously for any non-commutative group the best seed length was ≥ log n log(1/ε), even for a fixed order. 2) We give a reduction that "lifts" suitable generators for group products over G to a generator that fools width-w block products, i.e., tests of the form ∏ (g_i)^{f_i} where the f_i are arbitrary functions on disjoint blocks of w bits. Block products generalize several previously studied classes. The reduction applies to groups that are mixing in a representation-theoretic sense that we identify. 3) Combining (2) with (1) and other works we obtain new generators for block products over the quaternions or over any commutative group, with nearly optimal seed length. In particular, we obtain generators for read-once polynomials modulo any fixed m with nearly optimal seed length. Previously this was known only for m = 2. 4) We give a new generator for products over "mixing groups." The construction departs from previous work and uses representation theory. For constant error, we obtain optimal seed length, improving on previous work (which applied to any group). This paper identifies a challenge in the area that is reminiscent of a roadblock in circuit complexity - handling composite moduli - and points to several classes of groups to be attacked next.
Cite as

Chin Ho Lee and Emanuele Viola. Pseudorandom Bits for Non-Commutative Programs. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 9:1-9:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lee_et_al:LIPIcs.CCC.2025.9,
  author =	{Lee, Chin Ho and Viola, Emanuele},
  title =	{{Pseudorandom Bits for Non-Commutative Programs}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{9:1--9:22},
  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.2025.9},
  URN =		{urn:nbn:de:0030-drops-237039},
  doi =		{10.4230/LIPIcs.CCC.2025.9},
  annote =	{Keywords: Group programs, Space-bounded derandomization, Representation theory}
}
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