9 Search Results for "Sabin, Manuel"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.20
Samplability Makes Learning Easier

Authors: Guy Blanc, Caleb Koch, Jane Lange, Carmen Strassle, and Li-Yang Tan

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

Abstract
The standard definition of PAC learning (Valiant 1984) requires learners to succeed under all distributions - even ones that are intractable to sample from. This stands in contrast to samplable PAC learning (Blum, Furst, Kearns, and Lipton 1993), where learners only have to succeed under samplable distributions. We study this distinction and show that samplable PAC substantially expands the power of efficient learners. We first construct a concept class that requires exponential sample complexity in standard PAC but is learnable with polynomial sample complexity in samplable PAC. We then lift this statistical separation to the computational setting and obtain a separation relative to a random oracle. Our proofs center around a new complexity primitive, explicit evasive sets, that we introduce and study. These are sets for which membership is easy to determine but are extremely hard to sample from. Our results extend to the online setting to similarly show that its landscape changes when the adversary is assumed to be efficient instead of computationally unbounded.
Cite as

Guy Blanc, Caleb Koch, Jane Lange, Carmen Strassle, and Li-Yang Tan. Samplability Makes Learning Easier. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 20:1-20:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{blanc_et_al:LIPIcs.ITCS.2026.20,
  author =	{Blanc, Guy and Koch, Caleb and Lange, Jane and Strassle, Carmen and Tan, Li-Yang},
  title =	{{Samplability Makes Learning Easier}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{20:1--20:12},
  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.2026.20},
  URN =		{urn:nbn:de:0030-drops-253071},
  doi =		{10.4230/LIPIcs.ITCS.2026.20},
  annote =	{Keywords: PAC learning, Samplable distributions}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.95
The Planted Orthogonal Vectors Problem

Authors: David Kühnemann, Adam Polak, and Alon Rosen

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

Abstract
In the k-Orthogonal Vectors (k-OV) problem we are given k sets, each containing n binary vectors of dimension d = n^o(1), and our goal is to pick one vector from each set so that at each coordinate at least one vector has a zero. It is a central problem in fine-grained complexity, conjectured to require n^{k-o(1)} time in the worst case. We propose a way to plant a solution among vectors with i.i.d. p-biased entries, for appropriately chosen p, so that the planted solution is the unique one. Our conjecture is that the resulting k-OV instances still require time n^{k-o(1)} to solve, on average. Our planted distribution has the property that any subset of strictly less than k vectors has the same marginal distribution as in the model distribution, consisting of i.i.d. p-biased random vectors. We use this property to give average-case search-to-decision reductions for k-OV.
Cite as

David Kühnemann, Adam Polak, and Alon Rosen. The Planted Orthogonal Vectors Problem. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 95:1-95:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kuhnemann_et_al:LIPIcs.ESA.2025.95,
  author =	{K\"{u}hnemann, David and Polak, Adam and Rosen, Alon},
  title =	{{The Planted Orthogonal Vectors Problem}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{95:1--95:17},
  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.2025.95},
  URN =		{urn:nbn:de:0030-drops-245640},
  doi =		{10.4230/LIPIcs.ESA.2025.95},
  annote =	{Keywords: Average-case complexity, fine-grained complexity, orthogonal vectors}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.6
QSETH Strikes Again: Finer Quantum Lower Bounds for Lattice Problem, Strong Simulation, Hitting Set Problem, and More

Authors: Yanlin Chen, Yilei Chen, Rajendra Kumar, Subhasree Patro, and Florian Speelman

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

Abstract
Despite the wide range of problems for which quantum computers offer a computational advantage over their classical counterparts, there are also many problems for which the best known quantum algorithm provides a speedup that is only quadratic, or even subquadratic. Such a situation could also be desirable if we don't want quantum computers to solve certain problems fast - say problems relevant to post-quantum cryptography. When searching for algorithms and when analyzing the security of cryptographic schemes, we would like to have evidence that these problems are difficult to solve on quantum computers; but how do we assess the exact complexity of these problems? For most problems, there are no known ways to directly prove time lower bounds, however it can still be possible to relate the hardness of disparate problems to show conditional lower bounds. This approach has been popular in the classical community, and is being actively developed for the quantum case [Aaronson et al., 2020; Buhrman et al., 2021; Harry Buhrman et al., 2022; Andris Ambainis et al., 2022]. In this paper, by the use of the QSETH framework [Buhrman et al., 2021] we are able to understand the quantum complexity of a few natural variants of CNFSAT, such as parity-CNFSAT or counting-CNFSAT, and also are able to comment on the non-trivial complexity of approximate versions of counting-CNFSAT. Without considering such variants, the best quantum lower bounds will always be quadratically lower than the equivalent classical bounds, because of Grover’s algorithm; however, we are able to show that quantum algorithms will likely not attain even a quadratic speedup for many problems. These results have implications for the complexity of (variations of) lattice problems, the strong simulation and hitting set problems, and more. In the process, we explore the QSETH framework in greater detail and present a useful guide on how to effectively use the QSETH framework.
Cite as

Yanlin Chen, Yilei Chen, Rajendra Kumar, Subhasree Patro, and Florian Speelman. QSETH Strikes Again: Finer Quantum Lower Bounds for Lattice Problem, Strong Simulation, Hitting Set Problem, and More. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 6:1-6:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chen_et_al:LIPIcs.APPROX/RANDOM.2025.6,
  author =	{Chen, Yanlin and Chen, Yilei and Kumar, Rajendra and Patro, Subhasree and Speelman, Florian},
  title =	{{QSETH Strikes Again: Finer Quantum Lower Bounds for Lattice Problem, Strong Simulation, Hitting Set Problem, and More}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{6:1--6:24},
  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.2025.6},
  URN =		{urn:nbn:de:0030-drops-243723},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.6},
  annote =	{Keywords: Quantum conditional lower bounds, Fine-grained complexity, Lattice problems, Quantum strong simulation, Hitting set problem, QSETH}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.31
Towards Free Lunch Derandomization from Necessary Assumptions (And OWFs)

Authors: Marshall Ball, Lijie Chen, and Roei Tell

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

Abstract
The question of optimal derandomization, introduced by Doron et. al (JACM 2022), garnered significant recent attention. Works in recent years showed conditional superfast derandomization algorithms, as well as conditional impossibility results, and barriers for obtaining superfast derandomization using certain black-box techniques. Of particular interest is the extreme high-end, which focuses on "free lunch" derandomization, as suggested by Chen and Tell (FOCS 2021). This is derandomization that incurs essentially no time overhead, and errs only on inputs that are infeasible to find. Constructing such algorithms is challenging, and so far there have not been any results following the one in their initial work. In their result, their algorithm is essentially the classical Nisan-Wigderson generator, and they relied on an ad-hoc assumption asserting the existence of a function that is non-batch-computable over all polynomial-time samplable distributions. In this work we deduce free lunch derandomization from a variety of natural hardness assumptions. In particular, we do not resort to non-batch-computability, and the common denominator for all of our assumptions is hardness over all polynomial-time samplable distributions, which is necessary for the conclusion. The main technical components in our proofs are constructions of new and superfast targeted generators, which completely eliminate the time overheads that are inherent to all previously known constructions. In particular, we present an alternative construction for the targeted generator by Chen and Tell (FOCS 2021), which is faster than the original construction, and also more natural and technically intuitive. These contributions significantly strengthen the evidence for the possibility of free lunch derandomization, distill the required assumptions for such a result, and provide the first set of dedicated technical tools that are useful for studying the question.
Cite as

Marshall Ball, Lijie Chen, and Roei Tell. Towards Free Lunch Derandomization from Necessary Assumptions (And OWFs). In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 31:1-31:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ball_et_al:LIPIcs.CCC.2025.31,
  author =	{Ball, Marshall and Chen, Lijie and Tell, Roei},
  title =	{{Towards Free Lunch Derandomization from Necessary Assumptions (And OWFs)}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{31:1--31:20},
  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.2025.31},
  URN =		{urn:nbn:de:0030-drops-237259},
  doi =		{10.4230/LIPIcs.CCC.2025.31},
  annote =	{Keywords: Pseudorandomness, Derandomization}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.2
Hardness Amplification for Real-Valued Functions

Authors: Yunqi Li and Prashant Nalini Vasudevan

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

Abstract
Given an integer-valued function f:{0,1}ⁿ → {0,1,… , m-1} that is mildly hard to compute on instances drawn from some distribution D over {0,1}ⁿ, we show that the function g(x_1, … , x_t) = f(x_1) + ⋯ + f(x_t) is strongly hard to compute on instances (x_1,… ,x_t) drawn from the product distribution D^t. We also show the same for the task of approximately computing real-valued functions f:{0,1}ⁿ → [0,m). Our theorems immediately imply hardness self-amplification for several natural problems including Max-Clique and Max-SAT, Approximate #SAT, Entropy Estimation, etc..
Cite as

Yunqi Li and Prashant Nalini Vasudevan. Hardness Amplification for Real-Valued Functions. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 2:1-2:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{li_et_al:LIPIcs.CCC.2025.2,
  author =	{Li, Yunqi and Vasudevan, Prashant Nalini},
  title =	{{Hardness Amplification for Real-Valued Functions}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{2:1--2:25},
  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.2025.2},
  URN =		{urn:nbn:de:0030-drops-236967},
  doi =		{10.4230/LIPIcs.CCC.2025.2},
  annote =	{Keywords: Average-case complexity, hardness amplification}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.81
Worst-Case and Average-Case Hardness of Hypercycle and Database Problems

Authors: Cheng-Hao Fu, Andrea Lincoln, and Rene Reyes

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

Abstract
In this paper we present tight lower-bounds and new upper-bounds for hypergraph and database problems. We give tight lower-bounds for finding minimum hypercycles. We give tight lower-bounds for a substantial regime of unweighted hypercycle. We also give a new faster algorithm for longer unweighted hypercycles. We give a worst-case to average-case reduction from detecting a subgraph of a hypergraph in the worst-case to counting subgraphs of hypergraphs in the average-case. We demonstrate two applications of this worst-case to average-case reduction, which result in average-case lower bounds for counting counting hypercycles in random hypergraphs and queries in average-case databases. Our tight upper and lower bounds for hypercycle detection in the worst-case have immediate implications for the average-case via our worst-case to average-case reductions.
Cite as

Cheng-Hao Fu, Andrea Lincoln, and Rene Reyes. Worst-Case and Average-Case Hardness of Hypercycle and Database Problems. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 81:1-81:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fu_et_al:LIPIcs.ICALP.2025.81,
  author =	{Fu, Cheng-Hao and Lincoln, Andrea and Reyes, Rene},
  title =	{{Worst-Case and Average-Case Hardness of Hypercycle and Database Problems}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{81:1--81:20},
  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.2025.81},
  URN =		{urn:nbn:de:0030-drops-234581},
  doi =		{10.4230/LIPIcs.ICALP.2025.81},
  annote =	{Keywords: Hypergraphs, hypercycles, fine-grained complexity, average-case complexity, databases}
}
Document
Survey
DOI: 10.4230/TGDK.3.1.3
Uncertainty Management in the Construction of Knowledge Graphs: A Survey

Authors: Lucas Jarnac, Yoan Chabot, and Miguel Couceiro

Published in: TGDK, Volume 3, Issue 1 (2025). Transactions on Graph Data and Knowledge, Volume 3, Issue 1

Abstract
Knowledge Graphs (KGs) are a major asset for companies thanks to their great flexibility in data representation and their numerous applications, e.g., vocabulary sharing, Q&A or recommendation systems. To build a KG, it is a common practice to rely on automatic methods for extracting knowledge from various heterogeneous sources. However, in a noisy and uncertain world, knowledge may not be reliable and conflicts between data sources may occur. Integrating unreliable data would directly impact the use of the KG, therefore such conflicts must be resolved. This could be done manually by selecting the best data to integrate. This first approach is highly accurate, but costly and time-consuming. That is why recent efforts focus on automatic approaches, which represent a challenging task since it requires handling the uncertainty of extracted knowledge throughout its integration into the KG. We survey state-of-the-art approaches in this direction and present constructions of both open and enterprise KGs. We then describe different knowledge extraction methods and discuss downstream tasks after knowledge acquisition, including KG completion using embedding models, knowledge alignment, and knowledge fusion in order to address the problem of knowledge uncertainty in KG construction. We conclude with a discussion on the remaining challenges and perspectives when constructing a KG taking into account uncertainty.
Cite as

Lucas Jarnac, Yoan Chabot, and Miguel Couceiro. Uncertainty Management in the Construction of Knowledge Graphs: A Survey. In Transactions on Graph Data and Knowledge (TGDK), Volume 3, Issue 1, pp. 3:1-3:48, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{jarnac_et_al:TGDK.3.1.3,
  author =	{Jarnac, Lucas and Chabot, Yoan and Couceiro, Miguel},
  title =	{{Uncertainty Management in the Construction of Knowledge Graphs: A Survey}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{3:1--3:48},
  ISSN =	{2942-7517},
  year =	{2025},
  volume =	{3},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.3.1.3},
  URN =		{urn:nbn:de:0030-drops-233733},
  doi =		{10.4230/TGDK.3.1.3},
  annote =	{Keywords: Knowledge reconciliation, Uncertainty, Heterogeneous sources, Knowledge graph construction}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.68
Pseudorandomness and the Minimum Circuit Size Problem

Authors: Rahul Santhanam

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract
We explore the possibility of basing one-way functions on the average-case hardness of the fundamental Minimum Circuit Size Problem (MCSP[s]), which asks whether a Boolean function on n bits specified by its truth table has circuits of size s(n). 1) (Pseudorandomness from Zero-Error Average-Case Hardness) We show that for a given size function s, the following are equivalent: Pseudorandom distributions supported on strings describable by s(O(n))-size circuits exist; Hitting sets supported on strings describable by s(O(n))-size circuits exist; MCSP[s(O(n))] is zero-error average-case hard. Using similar techniques, we show that Feige’s hypothesis for random k-CNFs implies that there is a pseudorandom distribution (with constant error) supported entirely on satisfiable formulas. Underlying our results is a general notion of semantic sampling, which might be of independent interest. 2) (A New Conjecture) In analogy to a known universal construction of succinct hitting sets against arbitrary polynomial-size adversaries, we propose the Universality Conjecture: there is a universal construction of succinct pseudorandom distributions against arbitrary polynomial-size adversaries. We show that under the Universality Conjecture, the following are equivalent: One-way functions exist; Natural proofs useful against sub-exponential size circuits do not exist; Learning polynomial-size circuits with membership queries over the uniform distribution is hard; MCSP[2^(ε n)] is zero-error hard on average for some ε > 0; Cryptographic succinct hitting set generators exist. 3) (Non-Black-Box Results) We show that for weak circuit classes ℭ against which there are natural proofs [Alexander A. Razborov and Steven Rudich, 1997], pseudorandom functions secure against poly-size circuits in ℭ imply superpolynomial lower bounds in P against poly-size circuits in ℭ. We also show that for a certain natural variant of MCSP, there is a polynomial-time reduction from approximating the problem well in the worst case to solving it on average. These results are shown using non-black-box techniques, and in the first case we show that there is no black-box proof of the result under standard crypto assumptions.
Cite as

Rahul Santhanam. Pseudorandomness and the Minimum Circuit Size Problem. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 68:1-68:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{santhanam:LIPIcs.ITCS.2020.68,
  author =	{Santhanam, Rahul},
  title =	{{Pseudorandomness and the Minimum Circuit Size Problem}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{68:1--68:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.68},
  URN =		{urn:nbn:de:0030-drops-117532},
  doi =		{10.4230/LIPIcs.ITCS.2020.68},
  annote =	{Keywords: Minimum Circuit Size Problem, Pseudorandomness, Average-case Complexity, Natural Proofs, Universality Conjecture}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.27
Fine-Grained Derandomization: From Problem-Centric to Resource-Centric Complexity

Authors: Marco L. Carmosino, Russell Impagliazzo, and Manuel Sabin

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
We show that popular hardness conjectures about problems from the field of fine-grained complexity theory imply structural results for resource-based complexity classes. Namely, we show that if either k-Orthogonal Vectors or k-CLIQUE requires n^{epsilon k} time, for some constant epsilon>1/2, to count (note that these conjectures are significantly weaker than the usual ones made on these problems) on randomized machines for all but finitely many input lengths, then we have the following derandomizations: - BPP can be decided in polynomial time using only n^alpha random bits on average over any efficient input distribution, for any constant alpha>0 - BPP can be decided in polynomial time with no randomness on average over the uniform distribution This answers an open question of Ball et al. (STOC '17) in the positive of whether derandomization can be achieved from conjectures from fine-grained complexity theory. More strongly, these derandomizations improve over all previous ones achieved from worst-case uniform assumptions by succeeding on all but finitely many input lengths. Previously, derandomizations from worst-case uniform assumptions were only know to succeed on infinitely many input lengths. It is specifically the structure and moderate hardness of the k-Orthogonal Vectors and k-CLIQUE problems that makes removing this restriction possible. Via this uniform derandomization, we connect the problem-centric and resource-centric views of complexity theory by showing that exact hardness assumptions about specific problems like k-CLIQUE imply quantitative and qualitative relationships between randomized and deterministic time. This can be either viewed as a barrier to proving some of the main conjectures of fine-grained complexity theory lest we achieve a major breakthrough in unconditional derandomization or, optimistically, as route to attain such derandomizations by working on very concrete and weak conjectures about specific problems.
Cite as

Marco L. Carmosino, Russell Impagliazzo, and Manuel Sabin. Fine-Grained Derandomization: From Problem-Centric to Resource-Centric Complexity. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 27:1-27:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{carmosino_et_al:LIPIcs.ICALP.2018.27,
  author =	{Carmosino, Marco L. and Impagliazzo, Russell and Sabin, Manuel},
  title =	{{Fine-Grained Derandomization: From Problem-Centric to Resource-Centric Complexity}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{27:1--27:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.27},
  URN =		{urn:nbn:de:0030-drops-90316},
  doi =		{10.4230/LIPIcs.ICALP.2018.27},
  annote =	{Keywords: Derandomization, Hardness vs Randomness, Fine-Grained Complexity, Average-Case Complexity, k-Orthogonal Vectors, k-CLIQUE}
}
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