26 Search Results for "Lee, Chin Ho"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.30
New Bounds for Circular Trace Reconstruction

Authors: Arnav Burudgunte, Paul Valiant, and Hongao Wang

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

Abstract
The "trace reconstruction" problem asks, given an unknown binary string x and a channel that repeatedly returns "traces" of x with each bit randomly deleted with some probability p, how many traces are needed to recover x? There is an exponential gap between the best known upper and lower bounds for this problem. Many variants of the model have been introduced in hopes of motivating or revealing new approaches to narrow this gap. We study the variant of circular trace reconstruction introduced by Narayanan and Ren (ITCS 2021), in which traces undergo a random cyclic shift in addition to random deletions. We show an improved lower bound of Ω̃(n⁵) for circular trace reconstruction. This contrasts with the (previously) best known lower bounds of Ω̃(n³) in the circular case and Ω̃(n^{3/2}) in the linear case. Our bound shows the indistinguishability of traces from two sparse strings x,y that each have a constant number of nonzeros. Can this technique be extended significantly? How hard is it to reconstruct a sparse string x under a cyclic deletion channel? We resolve these questions by showing, using Fourier techniques, that Õ(n⁶) traces suffice for reconstructing any constant-sparse string in a circular deletion channel, in contrast to the best known upper bound of exp(Õ(n^{1/3})) for general strings in the circular deletion channel. This shows that new algorithms or new lower bounds must focus on non-constant-sparse strings.
Cite as

Arnav Burudgunte, Paul Valiant, and Hongao Wang. New Bounds for Circular Trace Reconstruction. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 30:1-30:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{burudgunte_et_al:LIPIcs.ITCS.2026.30,
  author =	{Burudgunte, Arnav and Valiant, Paul and Wang, Hongao},
  title =	{{New Bounds for Circular Trace Reconstruction}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{30:1--30:23},
  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.2026.30},
  URN =		{urn:nbn:de:0030-drops-253176},
  doi =		{10.4230/LIPIcs.ITCS.2026.30},
  annote =	{Keywords: Trace reconstruction, algorithmic statistics, Fourier analysis}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.21
Covering Weighted Points Using Unit Squares

Authors: Chaeyoon Chung, Jaegun Lee, and Hee-Kap Ahn

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
Given a set of n points in d-dimensional space, each assigned a positive weight, we study the problem of finding k axis-parallel unit hypercubes that maximize the total weight of the points contained in their union. In this paper, we present both exact and (1 - ε)-approximation algorithms for the case of k = 2. We present an exact algorithm that runs in O(n²) time in the plane, improving the previous O(n² log² n)-time result. This algorithm generalizes to higher dimensions and larger k in O(n^{dk/2}) time for fixed d and k. We also present a (1 - ε)-approximation algorithm that runs in O(n log min{n, 1/ε} + 1/ε³) time for k = 2 in the plane, improving the best known result. Our approximation algorithm also extends to higher dimensions.
Cite as

Chaeyoon Chung, Jaegun Lee, and Hee-Kap Ahn. Covering Weighted Points Using Unit Squares. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 21:1-21:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chung_et_al:LIPIcs.ISAAC.2025.21,
  author =	{Chung, Chaeyoon and Lee, Jaegun and Ahn, Hee-Kap},
  title =	{{Covering Weighted Points Using Unit Squares}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{21:1--21:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.21},
  URN =		{urn:nbn:de:0030-drops-249292},
  doi =		{10.4230/LIPIcs.ISAAC.2025.21},
  annote =	{Keywords: Maximum coverage, Unit squares, Approximation algorithms}
}
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
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}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.3
Near-Optimal Trace Reconstruction for Mildly Separated Strings

Authors: Anders Aamand, Allen Liu, and Shyam Narayanan

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

Abstract
In the trace reconstruction problem our goal is to learn an unknown string x ∈ {0,1}ⁿ given independent traces of x. A trace is obtained by independently deleting each bit of x with some probability δ and concatenating the remaining bits. It is a major open question whether the trace reconstruction problem can be solved with a polynomial number of traces when the deletion probability δ is constant. The best known upper bound and lower bounds are respectively exp(Õ(n^{1/5})) [Zachary Chase, 2021a] and ̃ Ω(n^{3/2}) [Zachary Chase, 2021b]. Our main result is that if the string x is mildly separated, meaning that the number of zeros between any two ones in x is at least polylog n, and if δ is a sufficiently small constant, then the trace reconstruction problem can be solved with O(n log n) traces and in polynomial time.
Cite as

Anders Aamand, Allen Liu, and Shyam Narayanan. Near-Optimal Trace Reconstruction for Mildly Separated Strings. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 3:1-3:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{aamand_et_al:LIPIcs.ICALP.2025.3,
  author =	{Aamand, Anders and Liu, Allen and Narayanan, Shyam},
  title =	{{Near-Optimal Trace Reconstruction for Mildly Separated Strings}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{3:1--3:20},
  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.2025.3},
  URN =		{urn:nbn:de:0030-drops-233801},
  doi =		{10.4230/LIPIcs.ICALP.2025.3},
  annote =	{Keywords: Trace Reconstruction, deletion channel, sample complexity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.68
New Pseudorandom Generators and Correlation Bounds Using Extractors

Authors: Vinayak M. Kumar

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

Abstract
We establish new correlation bounds and pseudorandom generators for a collection of computation models. These models are all natural generalization of structured low-degree 𝔽₂-polynomials that we did not have correlation bounds for before. In particular: - We construct a PRG for width-2 poly(n)-length branching programs which read d bits at a time with seed length 2^O(√{log n}) ⋅ d²log²(1/ε). This comes quadratically close to optimal dependence in d and log(1/ε). Improving the dependence on n would imply nontrivial PRGs for log n-degree 𝔽₂-polynomials. The previous PRG by Bogdanov, Dvir, Verbin, and Yehudayoff had an exponentially worse dependence on d with seed length of O(dlog n + d2^dlog(1/ε)). - We provide the first nontrivial (and nearly optimal) correlation bounds and PRGs against size-n^Ω(log n) AC⁰ circuits with either n^{.99} SYM gates (computing an arbitrary symmetric function) or n^{.49} THR gates (computing an arbitrary linear threshold function). This is a generalization of sparse 𝔽₂-polynomials, which can be simulated by an AC⁰ circuit with one parity gate at the top. Previous work of Servedio and Tan only handled n^{.49} SYM gates or n^{.24} THR gates, and previous work of Lovett and Srinivasan only handled polynomial-size circuits. - We give exponentially small correlation bounds against degree-n^O(1) 𝔽₂-polynomials which are set-multilinear over some arbitrary partition of the input into n^{1-O(1)} parts (noting that at n parts, we recover all low degree polynomials). This vastly generalizes correlation bounds against degree-d polynomials which are set-multilinear over a fixed partition into d blocks, which were established by Bhrushundi, Harsha, Hatami, Kopparty, and Kumar. The common technique behind all of these results is to fortify a hard function with the right type of extractor to obtain stronger correlation bounds for more general models of computation. Although this technique has been used in previous work, they rely on the model simplifying drastically under random restrictions. We view our results as a proof of concept that such fortification can be done even for classes that do not enjoy such behavior.
Cite as

Vinayak M. Kumar. New Pseudorandom Generators and Correlation Bounds Using Extractors. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 68:1-68:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kumar:LIPIcs.ITCS.2025.68,
  author =	{Kumar, Vinayak M.},
  title =	{{New Pseudorandom Generators and Correlation Bounds Using Extractors}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{68:1--68:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.68},
  URN =		{urn:nbn:de:0030-drops-226961},
  doi =		{10.4230/LIPIcs.ITCS.2025.68},
  annote =	{Keywords: Pseudorandom Generators, Correlation Bounds, Constant-Depth Circuits}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.52
Trace Reconstruction from Local Statistical Queries

Authors: Xi Chen, Anindya De, Chin Ho Lee, and Rocco A. Servedio

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

Abstract
The goal of trace reconstruction is to reconstruct an unknown n-bit string x given only independent random traces of x, where a random trace of x is obtained by passing x through a deletion channel. A Statistical Query (SQ) algorithm for trace reconstruction is an algorithm which can only access statistical information about the distribution of random traces of x rather than individual traces themselves. Such an algorithm is said to be 𝓁-local if each of its statistical queries corresponds to an 𝓁-junta function over some block of 𝓁 consecutive bits in the trace. Since several - but not all - known algorithms for trace reconstruction fall under the local statistical query paradigm, it is interesting to understand the abilities and limitations of local SQ algorithms for trace reconstruction. In this paper we establish nearly-matching upper and lower bounds on local Statistical Query algorithms for both worst-case and average-case trace reconstruction. For the worst-case problem, we show that there is an Õ(n^{1/5})-local SQ algorithm that makes all its queries with tolerance τ ≥ 2^{-Õ(n^{1/5})}, and also that any Õ(n^{1/5})-local SQ algorithm must make some query with tolerance τ ≤ 2^{-Ω̃(n^{1/5})}. For the average-case problem, we show that there is an O(log n)-local SQ algorithm that makes all its queries with tolerance τ ≥ 1/poly(n), and also that any O(log n)-local SQ algorithm must make some query with tolerance τ ≤ 1/poly(n).
Cite as

Xi Chen, Anindya De, Chin Ho Lee, and Rocco A. Servedio. Trace Reconstruction from Local Statistical Queries. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 52:1-52:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chen_et_al:LIPIcs.APPROX/RANDOM.2024.52,
  author =	{Chen, Xi and De, Anindya and Lee, Chin Ho and Servedio, Rocco A.},
  title =	{{Trace Reconstruction from Local Statistical Queries}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{52:1--52:24},
  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.2024.52},
  URN =		{urn:nbn:de:0030-drops-210459},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.52},
  annote =	{Keywords: trace reconstruction, statistical queries, algorithmic statistics}
}
Document
DOI: 10.4230/LIPIcs.CCC.2024.18
Pseudorandomness, Symmetry, Smoothing: I

Authors: Harm Derksen, Peter Ivanov, Chin Ho Lee, and Emanuele Viola

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract
We prove several new results about bounded uniform and small-bias distributions. A main message is that, small-bias, even perturbed with noise, does not fool several classes of tests better than bounded uniformity. We prove this for threshold tests, small-space algorithms, and small-depth circuits. In particular, we obtain small-bias distributions that - achieve an optimal lower bound on their statistical distance to any bounded-uniform distribution. This closes a line of research initiated by Alon, Goldreich, and Mansour in 2003, and improves on a result by O'Donnell and Zhao. - have heavier tail mass than the uniform distribution. This answers a question posed by several researchers including Bun and Steinke. - rule out a popular paradigm for constructing pseudorandom generators, originating in a 1989 work by Ajtai and Wigderson. This again answers a question raised by several researchers. For branching programs, our result matches a bound by Forbes and Kelley. Our small-bias distributions above are symmetric. We show that the xor of any two symmetric small-bias distributions fools any bounded function. Hence our examples cannot be extended to the xor of two small-bias distributions, another popular paradigm whose power remains unknown. We also generalize and simplify the proof of a result of Bazzi.
Cite as

Harm Derksen, Peter Ivanov, Chin Ho Lee, and Emanuele Viola. Pseudorandomness, Symmetry, Smoothing: I. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 18:1-18:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{derksen_et_al:LIPIcs.CCC.2024.18,
  author =	{Derksen, Harm and Ivanov, Peter and Lee, Chin Ho and Viola, Emanuele},
  title =	{{Pseudorandomness, Symmetry, Smoothing: I}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{18:1--18:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.18},
  URN =		{urn:nbn:de:0030-drops-204144},
  doi =		{10.4230/LIPIcs.CCC.2024.18},
  annote =	{Keywords: pseudorandomness, k-wise uniform distributions, small-bias distributions, noise, symmetric tests, thresholds, Krawtchouk polynomials}
}
Document
Survey
DOI: 10.4230/TGDK.1.1.11
How Does Knowledge Evolve in Open Knowledge Graphs?

Authors: Axel Polleres, Romana Pernisch, Angela Bonifati, Daniele Dell'Aglio, Daniil Dobriy, Stefania Dumbrava, Lorena Etcheverry, Nicolas Ferranti, Katja Hose, Ernesto Jiménez-Ruiz, Matteo Lissandrini, Ansgar Scherp, Riccardo Tommasini, and Johannes Wachs

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
Openly available, collaboratively edited Knowledge Graphs (KGs) are key platforms for the collective management of evolving knowledge. The present work aims t o provide an analysis of the obstacles related to investigating and processing specifically this central aspect of evolution in KGs. To this end, we discuss (i) the dimensions of evolution in KGs, (ii) the observability of evolution in existing, open, collaboratively constructed Knowledge Graphs over time, and (iii) possible metrics to analyse this evolution. We provide an overview of relevant state-of-the-art research, ranging from metrics developed for Knowledge Graphs specifically to potential methods from related fields such as network science. Additionally, we discuss technical approaches - and their current limitations - related to storing, analysing and processing large and evolving KGs in terms of handling typical KG downstream tasks.
Cite as

Axel Polleres, Romana Pernisch, Angela Bonifati, Daniele Dell'Aglio, Daniil Dobriy, Stefania Dumbrava, Lorena Etcheverry, Nicolas Ferranti, Katja Hose, Ernesto Jiménez-Ruiz, Matteo Lissandrini, Ansgar Scherp, Riccardo Tommasini, and Johannes Wachs. How Does Knowledge Evolve in Open Knowledge Graphs?. In Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge (TGDK), Volume 1, Issue 1, pp. 11:1-11:59, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{polleres_et_al:TGDK.1.1.11,
  author =	{Polleres, Axel and Pernisch, Romana and Bonifati, Angela and Dell'Aglio, Daniele and Dobriy, Daniil and Dumbrava, Stefania and Etcheverry, Lorena and Ferranti, Nicolas and Hose, Katja and Jim\'{e}nez-Ruiz, Ernesto and Lissandrini, Matteo and Scherp, Ansgar and Tommasini, Riccardo and Wachs, Johannes},
  title =	{{How Does Knowledge Evolve in Open Knowledge Graphs?}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{11:1--11:59},
  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.1.1.11},
  URN =		{urn:nbn:de:0030-drops-194855},
  doi =		{10.4230/TGDK.1.1.11},
  annote =	{Keywords: KG evolution, temporal KG, versioned KG, dynamic KG}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.44
On the Power of Regular and Permutation Branching Programs

Authors: Chin Ho Lee, Edward Pyne, and Salil Vadhan

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)

Abstract
We give new upper and lower bounds on the power of several restricted classes of arbitrary-order read-once branching programs (ROBPs) and standard-order ROBPs (SOBPs) that have received significant attention in the literature on pseudorandomness for space-bounded computation. - Regular SOBPs of length n and width ⌊w(n+1)/2⌋ can exactly simulate general SOBPs of length n and width w, and moreover an n/2-o(n) blow-up in width is necessary for such a simulation. Our result extends and simplifies prior average-case simulations (Reingold, Trevisan, and Vadhan (STOC 2006), Bogdanov, Hoza, Prakriya, and Pyne (CCC 2022)), in particular implying that weighted pseudorandom generators (Braverman, Cohen, and Garg (SICOMP 2020)) for regular SOBPs of width poly(n) or larger automatically extend to general SOBPs. Furthermore, our simulation also extends to general (even read-many) oblivious branching programs. - There exist natural functions computable by regular SOBPs of constant width that are average-case hard for permutation SOBPs of exponential width. Indeed, we show that Inner-Product mod 2 is average-case hard for arbitrary-order permutation ROBPs of exponential width. - There exist functions computable by constant-width arbitrary-order permutation ROBPs that are worst-case hard for exponential-width SOBPs. - Read-twice permutation branching programs of subexponential width can simulate polynomial-width arbitrary-order ROBPs.
Cite as

Chin Ho Lee, Edward Pyne, and Salil Vadhan. On the Power of Regular and Permutation Branching Programs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 44:1-44:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{lee_et_al:LIPIcs.APPROX/RANDOM.2023.44,
  author =	{Lee, Chin Ho and Pyne, Edward and Vadhan, Salil},
  title =	{{On the Power of Regular and Permutation Branching Programs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{44:1--44:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.44},
  URN =		{urn:nbn:de:0030-drops-188698},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.44},
  annote =	{Keywords: Pseudorandomness, Branching Programs}
}
Document
DOI: 10.4230/LIPIcs.CCC.2023.18
Tight Correlation Bounds for Circuits Between AC0 and TC0

Authors: Vinayak M. Kumar

Published in: LIPIcs, Volume 264, 38th Computational Complexity Conference (CCC 2023)

Abstract
We initiate the study of generalized AC⁰ circuits comprised of arbitrary unbounded fan-in gates which only need to be constant over inputs of Hamming weight ≥ k (up to negations of the input bits), which we denote GC⁰(k). The gate set of this class includes biased LTFs like the k-OR (outputs 1 iff ≥ k bits are 1) and k-AND (outputs 0 iff ≥ k bits are 0), and thus can be seen as an interpolation between AC⁰ and TC⁰. We establish a tight multi-switching lemma for GC⁰(k) circuits, which bounds the probability that several depth-2 GC⁰(k) circuits do not simultaneously simplify under a random restriction. We also establish a new depth reduction lemma such that coupled with our multi-switching lemma, we can show many results obtained from the multi-switching lemma for depth-d size-s AC⁰ circuits lifts to depth-d size-s^{.99} GC⁰(.01 log s) circuits with no loss in parameters (other than hidden constants). Our result has the following applications: - Size-2^Ω(n^{1/d}) depth-d GC⁰(Ω(n^{1/d})) circuits do not correlate with parity (extending a result of Håstad (SICOMP, 2014)). - Size-n^Ω(log n) GC⁰(Ω(log² n)) circuits with n^{.249} arbitrary threshold gates or n^{.499} arbitrary symmetric gates exhibit exponentially small correlation against an explicit function (extending a result of Tan and Servedio (RANDOM, 2019)). - There is a seed length O((log m)^{d-1}log(m/ε)log log(m)) pseudorandom generator against size-m depth-d GC⁰(log m) circuits, matching the AC⁰ lower bound of Håstad up to a log log m factor (extending a result of Lyu (CCC, 2022)). - Size-m GC⁰(log m) circuits have exponentially small Fourier tails (extending a result of Tal (CCC, 2017)).
Cite as

Vinayak M. Kumar. Tight Correlation Bounds for Circuits Between AC0 and TC0. In 38th Computational Complexity Conference (CCC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 264, pp. 18:1-18:40, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{kumar:LIPIcs.CCC.2023.18,
  author =	{Kumar, Vinayak M.},
  title =	{{Tight Correlation Bounds for Circuits Between AC0 and TC0}},
  booktitle =	{38th Computational Complexity Conference (CCC 2023)},
  pages =	{18:1--18:40},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-282-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{264},
  editor =	{Ta-Shma, Amnon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2023.18},
  URN =		{urn:nbn:de:0030-drops-182885},
  doi =		{10.4230/LIPIcs.CCC.2023.18},
  annote =	{Keywords: AC⁰, TC⁰, Switching Lemma, Lower Bounds, Correlation Bounds, Circuit Complexity}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.2
Fourier Growth of Regular Branching Programs

Authors: Chin Ho Lee, Edward Pyne, and Salil Vadhan

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)

Abstract
We analyze the Fourier growth, i.e. the L₁ Fourier weight at level k (denoted L_{1,k}), of read-once regular branching programs. We prove that every read-once regular branching program B of width w ∈ [1,∞] with s accepting states on n-bit inputs must have its L_{1,k} bounded by min{Pr[B(U_n) = 1](w-1)^k, s ⋅ O((n log n)/k)^{(k-1)/2}}. For any constant k, our result is tight up to constant factors for the AND function on w-1 bits, and is tight up to polylogarithmic factors for unbounded width programs. In particular, for k = 1 we have L_{1,1}(B) ≤ s, with no dependence on the width w of the program. Our result gives new bounds on the coin problem and new pseudorandom generators (PRGs). Furthermore, we obtain an explicit generator for unordered permutation branching programs of unbounded width with a constant factor stretch, where no PRG was previously known. Applying a composition theorem of Błasiok, Ivanov, Jin, Lee, Servedio and Viola (RANDOM 2021), we extend our results to "generalized group products," a generalization of modular sums and product tests.
Cite as

Chin Ho Lee, Edward Pyne, and Salil Vadhan. Fourier Growth of Regular Branching Programs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 2:1-2:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{lee_et_al:LIPIcs.APPROX/RANDOM.2022.2,
  author =	{Lee, Chin Ho and Pyne, Edward and Vadhan, Salil},
  title =	{{Fourier Growth of Regular Branching Programs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{2:1--2:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.2},
  URN =		{urn:nbn:de:0030-drops-171247},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.2},
  annote =	{Keywords: pseudorandomness, fourier analysis}
}
Document
DOI: 10.4230/LIPIcs.CCC.2022.3
Hitting Sets for Regular Branching Programs

Authors: Andrej Bogdanov, William M. Hoza, Gautam Prakriya, and Edward Pyne

Published in: LIPIcs, Volume 234, 37th Computational Complexity Conference (CCC 2022)

Abstract
We construct improved hitting set generators (HSGs) for ordered (read-once) regular branching programs in two parameter regimes. First, we construct an explicit ε-HSG for unbounded-width regular branching programs with a single accept state with seed length Õ(log n ⋅ log(1/ε)), where n is the length of the program. Second, we construct an explicit ε-HSG for width-w length-n regular branching programs with seed length Õ(log n ⋅ (√{log(1/ε)} + log w) + log(1/ε)). For context, the "baseline" in this area is the pseudorandom generator (PRG) by Nisan (Combinatorica 1992), which fools ordered (possibly non-regular) branching programs with seed length O(log(wn/ε) ⋅ log n). For regular programs, the state-of-the-art PRG, by Braverman, Rao, Raz, and Yehudayoff (FOCS 2010, SICOMP 2014), has seed length Õ(log(w/ε) ⋅ log n), which beats Nisan’s seed length when log(w/ε) = o(log n). Taken together, our two new constructions beat Nisan’s seed length in all parameter regimes except when log w and log(1/ε) are both Ω(log n) (for the construction of HSGs for regular branching programs with a single accept vertex). Extending work by Reingold, Trevisan, and Vadhan (STOC 2006), we furthermore show that an explicit HSG for regular branching programs with a single accept vertex with seed length o(log² n) in the regime log w = Θ(log(1/ε)) = Θ(log n) would imply improved HSGs for general ordered branching programs, which would be a major breakthrough in derandomization. Pyne and Vadhan (CCC 2021) recently obtained such parameters for the special case of permutation branching programs.
Cite as

Andrej Bogdanov, William M. Hoza, Gautam Prakriya, and Edward Pyne. Hitting Sets for Regular Branching Programs. In 37th Computational Complexity Conference (CCC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 234, pp. 3:1-3:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bogdanov_et_al:LIPIcs.CCC.2022.3,
  author =	{Bogdanov, Andrej and Hoza, William M. and Prakriya, Gautam and Pyne, Edward},
  title =	{{Hitting Sets for Regular Branching Programs}},
  booktitle =	{37th Computational Complexity Conference (CCC 2022)},
  pages =	{3:1--3:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-241-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{234},
  editor =	{Lovett, Shachar},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2022.3},
  URN =		{urn:nbn:de:0030-drops-165658},
  doi =		{10.4230/LIPIcs.CCC.2022.3},
  annote =	{Keywords: Pseudorandomness, hitting set generators, space-bounded computation}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.26
Bounded Indistinguishability for Simple Sources

Authors: Andrej Bogdanov, Krishnamoorthy Dinesh, Yuval Filmus, Yuval Ishai, Avi Kaplan, and Akshayaram Srinivasan

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract
A pair of sources X, Y over {0,1}ⁿ are k-indistinguishable if their projections to any k coordinates are identically distributed. Can some AC^0 function distinguish between two such sources when k is big, say k = n^{0.1}? Braverman’s theorem (Commun. ACM 2011) implies a negative answer when X is uniform, whereas Bogdanov et al. (Crypto 2016) observe that this is not the case in general. We initiate a systematic study of this question for natural classes of low-complexity sources, including ones that arise in cryptographic applications, obtaining positive results, negative results, and barriers. In particular: - There exist Ω(√n)-indistinguishable X, Y, samplable by degree-O(log n) polynomial maps (over F₂) and by poly(n)-size decision trees, that are Ω(1)-distinguishable by OR. - There exists a function f such that all f(d, ε)-indistinguishable X, Y that are samplable by degree-d polynomial maps are ε-indistinguishable by OR for all sufficiently large n. Moreover, f(1, ε) = ⌈log(1/ε)⌉ + 1 and f(2, ε) = O(log^{10}(1/ε)). - Extending (weaker versions of) the above negative results to AC^0 distinguishers would require settling a conjecture of Servedio and Viola (ECCC 2012). Concretely, if every pair of n^{0.9}-indistinguishable X, Y that are samplable by linear maps is ε-indistinguishable by AC^0 circuits, then the binary inner product function can have at most an ε-correlation with AC^0 ◦ ⊕ circuits. Finally, we motivate the question and our results by presenting applications of positive results to low-complexity secret sharing and applications of negative results to leakage-resilient cryptography.
Cite as

Andrej Bogdanov, Krishnamoorthy Dinesh, Yuval Filmus, Yuval Ishai, Avi Kaplan, and Akshayaram Srinivasan. Bounded Indistinguishability for Simple Sources. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 26:1-26:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bogdanov_et_al:LIPIcs.ITCS.2022.26,
  author =	{Bogdanov, Andrej and Dinesh, Krishnamoorthy and Filmus, Yuval and Ishai, Yuval and Kaplan, Avi and Srinivasan, Akshayaram},
  title =	{{Bounded Indistinguishability for Simple Sources}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{26:1--26:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.26},
  URN =		{urn:nbn:de:0030-drops-156223},
  doi =		{10.4230/LIPIcs.ITCS.2022.26},
  annote =	{Keywords: Pseudorandomness, bounded indistinguishability, complexity of sampling, constant-depth circuits, secret sharing, leakage-resilient cryptography}
}
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