7 Search Results for "Keller, Nathan"

Document
DOI: 10.4230/LIPIcs.ECOOP.2024.39
Formalizing, Mechanizing, and Verifying Class-Based Refinement Types

Authors: Ke Sun, Di Wang, Sheng Chen, Meng Wang, and Dan Hao

Published in: LIPIcs, Volume 313, 38th European Conference on Object-Oriented Programming (ECOOP 2024)

Abstract
Refinement types have been extensively used in class-based languages to specify and verify fine-grained logical specifications. Despite the advances in practical aspects such as applicability and usability, two fundamental issues persist. First, the soundness of existing class-based refinement type systems is inadequately explored, casting doubts on their reliability. Second, the expressiveness of existing systems is limited, restricting the depiction of semantic properties related to object-oriented constructs. This work tackles these issues through a systematic framework. We formalize a declarative class-based refinement type calculus (named RFJ), that is expressive and concise. We rigorously develop the soundness meta-theory of this calculus, followed by its mechanization in Coq. Finally, to ensure the calculus’s verifiability, we propose an algorithmic verification approach based on a fragment of first-order logic (named LFJ), and implement this approach as a type checker.
Cite as

Ke Sun, Di Wang, Sheng Chen, Meng Wang, and Dan Hao. Formalizing, Mechanizing, and Verifying Class-Based Refinement Types. In 38th European Conference on Object-Oriented Programming (ECOOP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 313, pp. 39:1-39:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{sun_et_al:LIPIcs.ECOOP.2024.39,
  author =	{Sun, Ke and Wang, Di and Chen, Sheng and Wang, Meng and Hao, Dan},
  title =	{{Formalizing, Mechanizing, and Verifying Class-Based Refinement Types}},
  booktitle =	{38th European Conference on Object-Oriented Programming (ECOOP 2024)},
  pages =	{39:1--39:30},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-341-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{313},
  editor =	{Aldrich, Jonathan and Salvaneschi, Guido},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2024.39},
  URN =		{urn:nbn:de:0030-drops-208881},
  doi =		{10.4230/LIPIcs.ECOOP.2024.39},
  annote =	{Keywords: Refinement Types, Program Verification, Object-oriented Programming}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.40
On Fourier Analysis of Sparse Boolean Functions over Certain Abelian Groups

Authors: Sourav Chakraborty, Swarnalipa Datta, Pranjal Dutta, Arijit Ghosh, and Swagato Sanyal

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
Given an Abelian group 𝒢, a Boolean-valued function f: 𝒢 → {-1,+1}, is said to be s-sparse, if it has at most s-many non-zero Fourier coefficients over the domain 𝒢. In a seminal paper, Gopalan et al. [Gopalan et al., 2011] proved "Granularity" for Fourier coefficients of Boolean valued functions over ℤ₂ⁿ, that have found many diverse applications in theoretical computer science and combinatorics. They also studied structural results for Boolean functions over ℤ₂ⁿ which are approximately Fourier-sparse. In this work, we obtain structural results for approximately Fourier-sparse Boolean valued functions over Abelian groups 𝒢 of the form, 𝒢: = ℤ_{p_1}^{n_1} × ⋯ × ℤ_{p_t}^{n_t}, for distinct primes p_i. We also obtain a lower bound of the form 1/(m²s)^⌈φ(m)/2⌉, on the absolute value of the smallest non-zero Fourier coefficient of an s-sparse function, where m = p_1 ⋯ p_t, and φ(m) = (p_1-1) ⋯ (p_t-1). We carefully apply probabilistic techniques from [Gopalan et al., 2011], to obtain our structural results, and use some non-trivial results from algebraic number theory to get the lower bound. We construct a family of at most s-sparse Boolean functions over ℤ_pⁿ, where p > 2, for arbitrarily large enough s, where the minimum non-zero Fourier coefficient is o(1/s). The "Granularity" result of Gopalan et al. implies that the absolute values of non-zero Fourier coefficients of any s-sparse Boolean valued function over ℤ₂ⁿ are Ω(1/s). So, our result shows that one cannot expect such a lower bound for general Abelian groups. Using our new structural results on the Fourier coefficients of sparse functions, we design an efficient sparsity testing algorithm for Boolean function, which tests whether the given function is s-sparse, or ε-far from any sparse Boolean function, and it requires poly((ms)^φ(m),1/ε)-many queries. Further, we generalize the notion of degree of a Boolean function over an Abelian group 𝒢. We use it to prove an Ω(√s) lower bound on the query complexity of any adaptive sparsity testing algorithm.
Cite as

Sourav Chakraborty, Swarnalipa Datta, Pranjal Dutta, Arijit Ghosh, and Swagato Sanyal. On Fourier Analysis of Sparse Boolean Functions over Certain Abelian Groups. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 40:1-40:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chakraborty_et_al:LIPIcs.MFCS.2024.40,
  author =	{Chakraborty, Sourav and Datta, Swarnalipa and Dutta, Pranjal and Ghosh, Arijit and Sanyal, Swagato},
  title =	{{On Fourier Analysis of Sparse Boolean Functions over Certain Abelian Groups}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{40:1--40:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.40},
  URN =		{urn:nbn:de:0030-drops-205963},
  doi =		{10.4230/LIPIcs.MFCS.2024.40},
  annote =	{Keywords: Fourier coefficients, sparse, Abelian, granularity}
}
Document
Survey
DOI: 10.4230/TGDK.2.1.1
Towards Representing Processes and Reasoning with Process Descriptions on the Web

Authors: Andreas Harth, Tobias Käfer, Anisa Rula, Jean-Paul Calbimonte, Eduard Kamburjan, and Martin Giese

Published in: TGDK, Volume 2, Issue 1 (2024): Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge, Volume 2, Issue 1

Abstract
We work towards a vocabulary to represent processes and temporal logic specifications as graph-structured data. Different fields use incompatible terminologies for describing essentially the same process-related concepts. In addition, processes can be represented from different perspectives and levels of abstraction: both state-centric and event-centric perspectives offer distinct insights into the underlying processes. In this work, we strive to unify the representation of processes and related concepts by leveraging the power of knowledge graphs. We survey approaches to representing processes and reasoning with process descriptions from different fields and provide a selection of scenarios to help inform the scope of a unified representation of processes. We focus on processes that can be executed and observed via web interfaces. We propose to provide a representation designed to combine state-centric and event-centric perspectives while incorporating temporal querying and reasoning capabilities on temporal logic specifications. A standardised vocabulary and representation for processes and temporal specifications would contribute towards bridging the gap between the terminologies from different fields and fostering the broader application of methods involving temporal logics, such as formal verification and program synthesis.
Cite as

Andreas Harth, Tobias Käfer, Anisa Rula, Jean-Paul Calbimonte, Eduard Kamburjan, and Martin Giese. Towards Representing Processes and Reasoning with Process Descriptions on the Web. In Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge (TGDK), Volume 2, Issue 1, pp. 1:1-1:32, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{harth_et_al:TGDK.2.1.1,
  author =	{Harth, Andreas and K\"{a}fer, Tobias and Rula, Anisa and Calbimonte, Jean-Paul and Kamburjan, Eduard and Giese, Martin},
  title =	{{Towards Representing Processes and Reasoning with Process Descriptions on the Web}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{1:1--1:32},
  ISSN =	{2942-7517},
  year =	{2024},
  volume =	{2},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.2.1.1},
  URN =		{urn:nbn:de:0030-drops-198583},
  doi =		{10.4230/TGDK.2.1.1},
  annote =	{Keywords: Process modelling, Process ontology, Temporal logic, Web services}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.27
Locality-Preserving Hashing for Shifts with Connections to Cryptography

Authors: Elette Boyle, Itai Dinur, Niv Gilboa, Yuval Ishai, Nathan Keller, and Ohad Klein

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

Abstract
Can we sense our location in an unfamiliar environment by taking a sublinear-size sample of our surroundings? Can we efficiently encrypt a message that only someone physically close to us can decrypt? To solve this kind of problems, we introduce and study a new type of hash functions for finding shifts in sublinear time. A function h:{0,1}ⁿ → ℤ_n is a (d,δ) locality-preserving hash function for shifts (LPHS) if: (1) h can be computed by (adaptively) querying d bits of its input, and (2) Pr[h(x) ≠ h(x ≪ 1) + 1] ≤ δ, where x is random and ≪ 1 denotes a cyclic shift by one bit to the left. We make the following contributions. - Near-optimal LPHS via Distributed Discrete Log. We establish a general two-way connection between LPHS and algorithms for distributed discrete logarithm in the generic group model. Using such an algorithm of Dinur et al. (Crypto 2018), we get LPHS with near-optimal error of δ = Õ(1/d²). This gives an unusual example for the usefulness of group-based cryptography in a post-quantum world. We extend the positive result to non-cyclic and worst-case variants of LPHS. - Multidimensional LPHS. We obtain positive and negative results for a multidimensional extension of LPHS, making progress towards an optimal 2-dimensional LPHS. - Applications. We demonstrate the usefulness of LPHS by presenting cryptographic and algorithmic applications. In particular, we apply multidimensional LPHS to obtain an efficient "packed" implementation of homomorphic secret sharing and a sublinear-time implementation of location-sensitive encryption whose decryption requires a significantly overlapping view.
Cite as

Elette Boyle, Itai Dinur, Niv Gilboa, Yuval Ishai, Nathan Keller, and Ohad Klein. Locality-Preserving Hashing for Shifts with Connections to Cryptography. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 27:1-27:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{boyle_et_al:LIPIcs.ITCS.2022.27,
  author =	{Boyle, Elette and Dinur, Itai and Gilboa, Niv and Ishai, Yuval and Keller, Nathan and Klein, Ohad},
  title =	{{Locality-Preserving Hashing for Shifts with Connections to Cryptography}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{27:1--27:24},
  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.2022.27},
  URN =		{urn:nbn:de:0030-drops-156231},
  doi =		{10.4230/LIPIcs.ITCS.2022.27},
  annote =	{Keywords: Sublinear algorithms, metric embeddings, shift finding, discrete logarithm, homomorphic secret sharing}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ICALP.2021.4
Error Resilient Space Partitioning (Invited Talk)

Authors: Orr Dunkelman, Zeev Geyzel, Chaya Keller, Nathan Keller, Eyal Ronen, Adi Shamir, and Ran J. Tessler

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
In this paper we consider a new type of space partitioning which bridges the gap between continuous and discrete spaces in an error resilient way. It is motivated by the problem of rounding noisy measurements from some continuous space such as ℝ^d to a discrete subset of representative values, in which each tile in the partition is defined as the preimage of one of the output points. Standard rounding schemes seem to be inherently discontinuous across tile boundaries, but in this paper we show how to make it perfectly consistent (with error resilience ε) by guaranteeing that any pair of consecutive measurements X₁ and X₂ whose L₂ distance is bounded by ε will be rounded to the same nearby representative point in the discrete output space. We achieve this resilience by allowing a few bits of information about the first measurement X₁ to be unidirectionally communicated to and used by the rounding process of the second measurement X₂. Minimizing this revealed information can be particularly important in privacy-sensitive applications such as COVID-19 contact tracing, in which we want to find out all the cases in which two persons were at roughly the same place at roughly the same time, by comparing cryptographically hashed versions of their itineraries in an error resilient way. The main problem we study in this paper is characterizing the achievable tradeoffs between the amount of information provided and the error resilience for various dimensions. We analyze the problem by considering the possible colored tilings of the space with k available colors, and use the color of the tile in which X₁ resides as the side information. We obtain our upper and lower bounds with a variety of techniques including isoperimetric inequalities, the Brunn-Minkowski theorem, sphere packing bounds, Sperner’s lemma, and Čech cohomology. In particular, we show that when X_i ∈ ℝ^d, communicating log₂(d+1) bits of information is both sufficient and necessary (in the worst case) to achieve positive resilience, and when d=3 we obtain a tight upper and lower asymptotic bound of (0.561 …)k^{1/3} on the achievable error resilience when we provide log₂(k) bits of information about X₁’s color.
Cite as

Orr Dunkelman, Zeev Geyzel, Chaya Keller, Nathan Keller, Eyal Ronen, Adi Shamir, and Ran J. Tessler. Error Resilient Space Partitioning (Invited Talk). In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 4:1-4:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{dunkelman_et_al:LIPIcs.ICALP.2021.4,
  author =	{Dunkelman, Orr and Geyzel, Zeev and Keller, Chaya and Keller, Nathan and Ronen, Eyal and Shamir, Adi and Tessler, Ran J.},
  title =	{{Error Resilient Space Partitioning}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{4:1--4:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.4},
  URN =		{urn:nbn:de:0030-drops-140731},
  doi =		{10.4230/LIPIcs.ICALP.2021.4},
  annote =	{Keywords: space partition, high-dimensional rounding, error resilience, sphere packing, Sperner’s lemma, Brunn-Minkowski theorem, \v{C}ech cohomology}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2021.69
Quantitative Correlation Inequalities via Semigroup Interpolation

Authors: Anindya De, Shivam Nadimpalli, and Rocco A. Servedio

Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)

Abstract
Most correlation inequalities for high-dimensional functions in the literature, such as the Fortuin-Kasteleyn-Ginibre inequality and the celebrated Gaussian Correlation Inequality of Royen, are qualitative statements which establish that any two functions of a certain type have non-negative correlation. We give a general approach that can be used to bootstrap many qualitative correlation inequalities for functions over product spaces into quantitative statements. The approach combines a new extremal result about power series, proved using complex analysis, with harmonic analysis of functions over product spaces. We instantiate this general approach in several different concrete settings to obtain a range of new and near-optimal quantitative correlation inequalities, including: - A {quantitative} version of Royen’s celebrated Gaussian Correlation Inequality [Royen, 2014]. In [Royen, 2014] Royen confirmed a conjecture, open for 40 years, stating that any two symmetric convex sets must be non-negatively correlated under any centered Gaussian distribution. We give a lower bound on the correlation in terms of the vector of degree-2 Hermite coefficients of the two convex sets, conceptually similar to Talagrand’s quantitative correlation bound for monotone Boolean functions over {0,1}ⁿ [M. Talagrand, 1996]. We show that our quantitative version of Royen’s theorem is within a logarithmic factor of being optimal. - A quantitative version of the well-known FKG inequality for monotone functions over any finite product probability space. This is a broad generalization of Talagrand’s quantitative correlation bound for functions from {0,1}ⁿ to {0,1} under the uniform distribution [M. Talagrand, 1996]; the only prior generalization of which we are aware is due to Keller [Nathan Keller, 2012; Keller, 2008; Nathan Keller, 2009], which extended [M. Talagrand, 1996] to product distributions over {0,1}ⁿ. In the special case of p-biased distributions over {0,1}ⁿ that was considered by Keller, our new bound essentially saves a factor of p log(1/p) over the quantitative bounds given in [Nathan Keller, 2012; Keller, 2008; Nathan Keller, 2009]. We also give {a quantitative version of} the FKG inequality for monotone functions over the continuous domain [0,1]ⁿ, answering a question of Keller [Nathan Keller, 2009].
Cite as

Anindya De, Shivam Nadimpalli, and Rocco A. Servedio. Quantitative Correlation Inequalities via Semigroup Interpolation. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 69:1-69:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{de_et_al:LIPIcs.ITCS.2021.69,
  author =	{De, Anindya and Nadimpalli, Shivam and Servedio, Rocco A.},
  title =	{{Quantitative Correlation Inequalities via Semigroup Interpolation}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{69:1--69:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{Lee, James R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.69},
  URN =		{urn:nbn:de:0030-drops-136081},
  doi =		{10.4230/LIPIcs.ITCS.2021.69},
  annote =	{Keywords: complex analysis, correlation inequality, FKG inequality, Gaussian correlation inequality, harmonic analysis, Markov semigroups}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.13
Tight Bounds on Online Checkpointing Algorithms

Authors: Achiya Bar-On, Itai Dinur, Orr Dunkelman, Rani Hod, Nathan Keller, Eyal Ronen, and Adi Shamir

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

Abstract
The problem of online checkpointing is a classical problem with numerous applications which had been studied in various forms for almost 50 years. In the simplest version of this problem, a user has to maintain k memorized checkpoints during a long computation, where the only allowed operation is to move one of the checkpoints from its old time to the current time, and his goal is to keep the checkpoints as evenly spread out as possible at all times. At ICALP'13 Bringmann et al. studied this problem as a special case of an online/offline optimization problem in which the deviation from uniformity is measured by the natural discrepancy metric of the worst case ratio between real and ideal segment lengths. They showed this discrepancy is smaller than 1.59-o(1) for all k, and smaller than ln4-o(1)~~1.39 for the sparse subset of k's which are powers of 2. In addition, they obtained upper bounds on the achievable discrepancy for some small values of k. In this paper we solve the main problems left open in the ICALP'13 paper by proving that ln4 is a tight upper and lower bound on the asymptotic discrepancy for all large k, and by providing tight upper and lower bounds (in the form of provably optimal checkpointing algorithms, some of which are in fact better than those of Bringmann et al.) for all the small values of k <= 10.
Cite as

Achiya Bar-On, Itai Dinur, Orr Dunkelman, Rani Hod, Nathan Keller, Eyal Ronen, and Adi Shamir. Tight Bounds on Online Checkpointing Algorithms. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 13:1-13:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{baron_et_al:LIPIcs.ICALP.2018.13,
  author =	{Bar-On, Achiya and Dinur, Itai and Dunkelman, Orr and Hod, Rani and Keller, Nathan and Ronen, Eyal and Shamir, Adi},
  title =	{{Tight Bounds on Online Checkpointing Algorithms}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{13:1--13:13},
  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.2018.13},
  URN =		{urn:nbn:de:0030-drops-90179},
  doi =		{10.4230/LIPIcs.ICALP.2018.13},
  annote =	{Keywords: checkpoint, checkpointing algorithm, online algorithm, uniform distribution, discrepancy}
}
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