46 Search Results for "Ball, Thomas"


Volume

LIPIcs, Volume 32

1st Summit on Advances in Programming Languages (SNAPL 2015)

SNAPL 2015, May 3-6, 2015, Asilomar, California, US

Editors: Thomas Ball, Rastislav Bodík, Shriram Krishnamurthi, Benjamin S. Lerner, and Greg Morriset

Document
Track A: Algorithms, Complexity and Games
Exploiting Automorphisms of Temporal Graphs for Fast Exploration and Rendezvous

Authors: Konstantinos Dogeas, Thomas Erlebach, Frank Kammer, Johannes Meintrup, and William K. Moses Jr.

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)


Abstract
Temporal graphs are dynamic graphs where the edge set can change in each time step, while the vertex set stays the same. Exploration of temporal graphs whose snapshot in each time step is a connected graph, called connected temporal graphs, has been widely studied. In this paper, we extend the concept of graph automorphisms from static graphs to temporal graphs and show for the first time that symmetries enable faster exploration: We prove that a connected temporal graph with n vertices and orbit number r (i.e., r is the number of automorphism orbits) can be explored in O(r n^{1+ε}) time steps, for any fixed ε > 0. For r = O(n^c) for constant c < 1, this is a significant improvement over the known tight worst-case bound of Θ(n²) time steps for arbitrary connected temporal graphs. We also give two lower bounds for temporal exploration, showing that Ω(n log n) time steps are required for some inputs with r = O(1) and that Ω(rn) time steps are required for some inputs for any r with 1 ≤ r ≤ n. Moreover, we show that the techniques we develop for fast exploration can be used to derive the following result for rendezvous: Two agents with different programs and without communication ability are placed by an adversary at arbitrary vertices and given full information about the connected temporal graph, except that they do not have consistent vertex labels. Then the two agents can meet at a common vertex after O(n^{1+ε}) time steps, for any constant ε > 0. For some connected temporal graphs with the orbit number being a constant, we also present a complementary lower bound of Ω(nlog n) time steps.

Cite as

Konstantinos Dogeas, Thomas Erlebach, Frank Kammer, Johannes Meintrup, and William K. Moses Jr.. Exploiting Automorphisms of Temporal Graphs for Fast Exploration and Rendezvous. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 55:1-55:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{dogeas_et_al:LIPIcs.ICALP.2024.55,
  author =	{Dogeas, Konstantinos and Erlebach, Thomas and Kammer, Frank and Meintrup, Johannes and Moses Jr., William K.},
  title =	{{Exploiting Automorphisms of Temporal Graphs for Fast Exploration and Rendezvous}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{55:1--55:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.55},
  URN =		{urn:nbn:de:0030-drops-201989},
  doi =		{10.4230/LIPIcs.ICALP.2024.55},
  annote =	{Keywords: dynamic graphs, parameterized algorithms, algorithmic graph theory, graph automorphism, orbit number}
}
Document
Track A: Algorithms, Complexity and Games
Better Sparsifiers for Directed Eulerian Graphs

Authors: Sushant Sachdeva, Anvith Thudi, and Yibin Zhao

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)


Abstract
Spectral sparsification for directed Eulerian graphs is a key component in the design of fast algorithms for solving directed Laplacian linear systems. Directed Laplacian linear system solvers are crucial algorithmic primitives to fast computation of fundamental problems on random walks, such as computing stationary distributions, hitting and commute times, and personalized PageRank vectors. While spectral sparsification is well understood for undirected graphs and it is known that for every graph G, (1+ε)-sparsifiers with O(nε^{-2}) edges exist [Batson-Spielman-Srivastava, STOC '09] (which is optimal), the best known constructions of Eulerian sparsifiers require Ω(nε^{-2}log⁴ n) edges and are based on short-cycle decompositions [Chu et al., FOCS '18]. In this paper, we give improved constructions of Eulerian sparsifiers, specifically: 1) We show that for every directed Eulerian graph G→, there exists an Eulerian sparsifier with O(nε^{-2} log² n log²log n + nε^{-4/3}log^{8/3} n) edges. This result is based on combining short-cycle decompositions [Chu-Gao-Peng-Sachdeva-Sawlani-Wang, FOCS '18, SICOMP] and [Parter-Yogev, ICALP '19], with recent progress on the matrix Spencer conjecture [Bansal-Meka-Jiang, STOC '23]. 2) We give an improved analysis of the constructions based on short-cycle decompositions, giving an m^{1+δ}-time algorithm for any constant δ > 0 for constructing Eulerian sparsifiers with O(nε^{-2}log³ n) edges.

Cite as

Sushant Sachdeva, Anvith Thudi, and Yibin Zhao. Better Sparsifiers for Directed Eulerian Graphs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 119:1-119:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{sachdeva_et_al:LIPIcs.ICALP.2024.119,
  author =	{Sachdeva, Sushant and Thudi, Anvith and Zhao, Yibin},
  title =	{{Better Sparsifiers for Directed Eulerian Graphs}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{119:1--119:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.119},
  URN =		{urn:nbn:de:0030-drops-202628},
  doi =		{10.4230/LIPIcs.ICALP.2024.119},
  annote =	{Keywords: Graph algorithms, Linear algebra and computation, Discrepancy theory}
}
Document
The Localized Union-Of-Balls Bifiltration

Authors: Michael Kerber and Matthias Söls

Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)


Abstract
We propose an extension of the classical union-of-balls filtration of persistent homology: fixing a point q, we focus our attention to a ball centered at q whose radius is controlled by a second scale parameter. We discuss an absolute variant, where the union is just restricted to the q-ball, and a relative variant where the homology of the q-ball relative to its boundary is considered. Interestingly, these natural constructions lead to bifiltered simplicial complexes which are not k-critical for any finite k. Nevertheless, we demonstrate that these bifiltrations can be computed exactly and efficiently, and we provide a prototypical implementation using the CGAL library. We also argue that some of the recent algorithmic advances for 2-parameter persistence (which usually assume k-criticality for some finite k) carry over to the ∞-critical case.

Cite as

Michael Kerber and Matthias Söls. The Localized Union-Of-Balls Bifiltration. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 45:1-45:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{kerber_et_al:LIPIcs.SoCG.2023.45,
  author =	{Kerber, Michael and S\"{o}ls, Matthias},
  title =	{{The Localized Union-Of-Balls Bifiltration}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{45:1--45:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.45},
  URN =		{urn:nbn:de:0030-drops-178953},
  doi =		{10.4230/LIPIcs.SoCG.2023.45},
  annote =	{Keywords: Topological Data Analysis, Multi-Parameter Persistence, Persistent Local Homology}
}
Document
Tight Bounds for Repeated Balls-Into-Bins

Authors: Dimitrios Los and Thomas Sauerwald

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)


Abstract
We study the repeated balls-into-bins process introduced by Becchetti, Clementi, Natale, Pasquale and Posta (2019). This process starts with m balls arbitrarily distributed across n bins. At each round t = 1,2,…, one ball is selected from each non-empty bin, and then placed it into a bin chosen independently and uniformly at random. We prove the following results: - For any n ⩽ m ⩽ poly(n), we prove a lower bound of Ω(m/n ⋅ log n) on the maximum load. For the special case m = n, this matches the upper bound of 𝒪(log n), as shown in [Luca Becchetti et al., 2019]. It also provides a positive answer to the conjecture in [Luca Becchetti et al., 2019] that for m = n the maximum load is ω(log n/ log log n) at least once in a polynomially large time interval. For m ∈ [ω(n), n log n], our new lower bound disproves the conjecture in [Luca Becchetti et al., 2019] that the maximum load remains 𝒪(log n). - For any n ⩽ m ⩽ poly(n), we prove an upper bound of 𝒪(m/n ⋅ log n) on the maximum load for all steps of a polynomially large time interval. This matches our lower bound up to multiplicative constants. - For any m ⩾ n, our analysis also implies an 𝒪(m²/n) waiting time to reach a configuration with a 𝒪(m/n ⋅ log m) maximum load, even for worst-case initial distributions. - For m ⩾ n, we show that every ball visits every bin in 𝒪(m log m) rounds. For m = n, this improves the previous upper bound of 𝒪(n log² n) in [Luca Becchetti et al., 2019]. We also prove that the upper bound is tight up to multiplicative constants for any n ⩽ m ⩽ poly(n).

Cite as

Dimitrios Los and Thomas Sauerwald. Tight Bounds for Repeated Balls-Into-Bins. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 45:1-45:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{los_et_al:LIPIcs.STACS.2023.45,
  author =	{Los, Dimitrios and Sauerwald, Thomas},
  title =	{{Tight Bounds for Repeated Balls-Into-Bins}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{45:1--45:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.45},
  URN =		{urn:nbn:de:0030-drops-176975},
  doi =		{10.4230/LIPIcs.STACS.2023.45},
  annote =	{Keywords: Repeated balls-into-bins, self-stabilizing systems, balanced allocations, potential functions, random walks}
}
Document
Balanced Allocations with Incomplete Information: The Power of Two Queries

Authors: Dimitrios Los and Thomas Sauerwald

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


Abstract
We consider the allocation of m balls into n bins with incomplete information. In the classical Two-Choice process a ball first queries the load of two randomly chosen bins and is then placed in the least loaded bin. In our setting, each ball also samples two random bins but can only estimate a bin’s load by sending binary queries of the form "Is the load at least the median?" or "Is the load at least 100?". For the lightly loaded case m = 𝒪(n), Feldheim and Gurel-Gurevich (2021) showed that with one query it is possible to achieve a maximum load of 𝒪(√{log n/log log n}), and they also pose the question whether a maximum load of m/n+𝒪(√{log n/log log n}) is possible for any m = Ω(n). In this work, we resolve this open problem by proving a lower bound of m/n+Ω(√{log n}) for a fixed m = Θ(n √{log n}), and a lower bound of m/n+Ω(log n/log log n) for some m depending on the used strategy. We complement this negative result by proving a positive result for multiple queries. In particular, we show that with only two binary queries per chosen bin, there is an oblivious strategy which ensures a maximum load of m/n+𝒪(√{log n}) for any m ≥ 1. Further, for any number of k = 𝒪(log log n) binary queries, the upper bound on the maximum load improves to m/n + 𝒪(k(log n)^{1/k}) for any m ≥ 1. This result for k queries has several interesting consequences: (i) it implies new bounds for the (1+β)-process introduced by Peres, Talwar and Wieder (2015), (ii) it leads to new bounds for the graphical balanced allocation process on dense expander graphs, and (iii) it recovers and generalizes the bound of m/n+𝒪(log log n) on the maximum load achieved by the Two-Choice process, including the heavily loaded case m = Ω(n) which was derived in previous works by Berenbrink et al. (2006) as well as Talwar and Wieder (2014). One novel aspect of our proofs is the use of multiple super-exponential potential functions, which might be of use in future work.

Cite as

Dimitrios Los and Thomas Sauerwald. Balanced Allocations with Incomplete Information: The Power of Two Queries. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 103:1-103:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{los_et_al:LIPIcs.ITCS.2022.103,
  author =	{Los, Dimitrios and Sauerwald, Thomas},
  title =	{{Balanced Allocations with Incomplete Information: The Power of Two Queries}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{103:1--103:23},
  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.2022.103},
  URN =		{urn:nbn:de:0030-drops-156994},
  doi =		{10.4230/LIPIcs.ITCS.2022.103},
  annote =	{Keywords: power-of-two-choices, balanced allocations, potential functions, thinning}
}
Document
Low Diameter Graph Decompositions by Approximate Distance Computation

Authors: Ruben Becker, Yuval Emek, and Christoph Lenzen

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


Abstract
In many models for large-scale computation, decomposition of the problem is key to efficient algorithms. For distance-related graph problems, it is often crucial that such a decomposition results in clusters of small diameter, while the probability that an edge is cut by the decomposition scales linearly with the length of the edge. There is a large body of literature on low diameter graph decomposition with small edge cutting probabilities, with all existing techniques heavily building on single source shortest paths (SSSP) computations. Unfortunately, in many theoretical models for large-scale computations, the SSSP task constitutes a complexity bottleneck. Therefore, it is desirable to replace exact SSSP computations with approximate ones. However this imposes a fundamental challenge since the existing constructions of low diameter graph decomposition with small edge cutting probabilities inherently rely on the subtractive form of the triangle inequality, which fails to hold under distance approximation. The current paper overcomes this obstacle by developing a technique termed blurry ball growing. By combining this technique with a clever algorithmic idea of Miller et al. (SPAA 2013), we obtain a construction of low diameter decompositions with small edge cutting probabilities which replaces exact SSSP computations by (a small number of) approximate ones. The utility of our approach is showcased by deriving efficient algorithms that work in the CONGEST, PRAM, and semi-streaming models of computation. As an application, we obtain metric tree embedding algorithms in the vein of Bartal (FOCS 1996) whose computational complexities in these models are optimal up to polylogarithmic factors. Our embeddings have the additional useful property that the tree can be mapped back to the original graph such that each edge is "used" only logaritmically many times, which is of interest for capacitated problems and simulating CONGEST algorithms on the tree into which the graph is embedded.

Cite as

Ruben Becker, Yuval Emek, and Christoph Lenzen. Low Diameter Graph Decompositions by Approximate Distance Computation. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 50:1-50:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{becker_et_al:LIPIcs.ITCS.2020.50,
  author =	{Becker, Ruben and Emek, Yuval and Lenzen, Christoph},
  title =	{{Low Diameter Graph Decompositions by Approximate Distance Computation}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{50:1--50:29},
  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.2020.50},
  URN =		{urn:nbn:de:0030-drops-117355},
  doi =		{10.4230/LIPIcs.ITCS.2020.50},
  annote =	{Keywords: graph decompositions, metric tree embeddings, distributed graph algorithms, parallel graph algorithms, (semi-)streaming graph algorithms}
}
Document
Limits to Non-Malleability

Authors: Marshall Ball, Dana Dachman-Soled, Mukul Kulkarni, and Tal Malkin

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


Abstract
There have been many successes in constructing explicit non-malleable codes for various classes of tampering functions in recent years, and strong existential results are also known. In this work we ask the following question: When can we rule out the existence of a non-malleable code for a tampering class ℱ? First, we start with some classes where positive results are well-known, and show that when these classes are extended in a natural way, non-malleable codes are no longer possible. Specifically, we show that no non-malleable codes exist for any of the following tampering classes: - Functions that change d/2 symbols, where d is the distance of the code; - Functions where each input symbol affects only a single output symbol; - Functions where each of the n output bits is a function of n-log n input bits. Furthermore, we rule out constructions of non-malleable codes for certain classes ℱ via reductions to the assumption that a distributional problem is hard for ℱ, that make black-box use of the tampering functions in the proof. In particular, this yields concrete obstacles for the construction of efficient codes for NC, even assuming average-case variants of P ⊈ NC.

Cite as

Marshall Ball, Dana Dachman-Soled, Mukul Kulkarni, and Tal Malkin. Limits to Non-Malleability. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 80:1-80:32, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{ball_et_al:LIPIcs.ITCS.2020.80,
  author =	{Ball, Marshall and Dachman-Soled, Dana and Kulkarni, Mukul and Malkin, Tal},
  title =	{{Limits to Non-Malleability}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{80:1--80:32},
  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.2020.80},
  URN =		{urn:nbn:de:0030-drops-117657},
  doi =		{10.4230/LIPIcs.ITCS.2020.80},
  annote =	{Keywords: non-malleable codes, black-box impossibility, tamper-resilient cryptogtaphy, average-case hardness}
}
Document
Cryptography from Information Loss

Authors: Marshall Ball, Elette Boyle, Akshay Degwekar, Apoorvaa Deshpande, Alon Rosen, Vinod Vaikuntanathan, and Prashant Nalini Vasudevan

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


Abstract
Reductions between problems, the mainstay of theoretical computer science, efficiently map an instance of one problem to an instance of another in such a way that solving the latter allows solving the former. The subject of this work is "lossy" reductions, where the reduction loses some information about the input instance. We show that such reductions, when they exist, have interesting and powerful consequences for lifting hardness into "useful" hardness, namely cryptography. Our first, conceptual, contribution is a definition of lossy reductions in the language of mutual information. Roughly speaking, our definition says that a reduction C is t-lossy if, for any distribution X over its inputs, the mutual information I(X;C(X)) ≤ t. Our treatment generalizes a variety of seemingly related but distinct notions such as worst-case to average-case reductions, randomized encodings (Ishai and Kushilevitz, FOCS 2000), homomorphic computations (Gentry, STOC 2009), and instance compression (Harnik and Naor, FOCS 2006). We then proceed to show several consequences of lossy reductions: 1. We say that a language L has an f-reduction to a language L' for a Boolean function f if there is a (randomized) polynomial-time algorithm C that takes an m-tuple of strings X = (x_1,…,x_m), with each x_i ∈ {0,1}^n, and outputs a string z such that with high probability, L'(z) = f(L(x_1),L(x_2),…,L(x_m)). Suppose a language L has an f-reduction C to L' that is t-lossy. Our first result is that one-way functions exist if L is worst-case hard and one of the following conditions holds: - f is the OR function, t ≤ m/100, and L' is the same as L - f is the Majority function, and t ≤ m/100 - f is the OR function, t ≤ O(m log n), and the reduction has no error This improves on the implications that follow from combining (Drucker, FOCS 2012) with (Ostrovsky and Wigderson, ISTCS 1993) that result in auxiliary-input one-way functions. 2. Our second result is about the stronger notion of t-compressing f-reductions - reductions that only output t bits. We show that if there is an average-case hard language L that has a t-compressing Majority reduction to some language for t=m/100, then there exist collision-resistant hash functions. This improves on the result of (Harnik and Naor, STOC 2006), whose starting point is a cryptographic primitive (namely, one-way functions) rather than average-case hardness, and whose assumption is a compressing OR-reduction of SAT (which is now known to be false unless the polynomial hierarchy collapses). Along the way, we define a non-standard one-sided notion of average-case hardness, which is the notion of hardness used in the second result above, that may be of independent interest.

Cite as

Marshall Ball, Elette Boyle, Akshay Degwekar, Apoorvaa Deshpande, Alon Rosen, Vinod Vaikuntanathan, and Prashant Nalini Vasudevan. Cryptography from Information Loss. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 81:1-81:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{ball_et_al:LIPIcs.ITCS.2020.81,
  author =	{Ball, Marshall and Boyle, Elette and Degwekar, Akshay and Deshpande, Apoorvaa and Rosen, Alon and Vaikuntanathan, Vinod and Vasudevan, Prashant Nalini},
  title =	{{Cryptography from Information Loss}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{81:1--81:27},
  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.2020.81},
  URN =		{urn:nbn:de:0030-drops-117667},
  doi =		{10.4230/LIPIcs.ITCS.2020.81},
  annote =	{Keywords: Compression, Information Loss, One-Way Functions, Reductions, Generic Constructions}
}
Document
On the Complexity of Decomposable Randomized Encodings, Or: How Friendly Can a Garbling-Friendly PRF Be?

Authors: Marshall Ball, Justin Holmgren, Yuval Ishai, Tianren Liu, and Tal Malkin

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


Abstract
Garbling schemes, also known as decomposable randomized encodings (DRE), have found many applications in cryptography. However, despite a large body of work on constructing such schemes, very little is known about their limitations. We initiate a systematic study of the DRE complexity of Boolean functions, obtaining the following main results: - Near-quadratic lower bounds. We use a classical lower bound technique of Nečiporuk [Dokl. Akad. Nauk SSSR '66] to show an Ω(n²/log n) lower bound on the size of any DRE for many explicit Boolean functions. For some natural functions, we obtain a corresponding upper bound, thus settling their DRE complexity up to polylogarithmic factors. Prior to our work, no superlinear lower bounds were known, even for non-explicit functions. - Garbling-friendly PRFs. We show that any exponentially secure PRF has Ω(n²/log n) DRE size, and present a plausible candidate for a "garbling-optimal" PRF that nearly meets this bound. This candidate establishes a barrier for super-quadratic DRE lower bounds via natural proof techniques. In contrast, we show a candidate for a weak PRF with near-exponential security and linear DRE size. Our results establish several qualitative separations, including near-quadratic separations between computational and information-theoretic DRE size of Boolean functions, and between DRE size of weak vs. strong PRFs.

Cite as

Marshall Ball, Justin Holmgren, Yuval Ishai, Tianren Liu, and Tal Malkin. On the Complexity of Decomposable Randomized Encodings, Or: How Friendly Can a Garbling-Friendly PRF Be?. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 86:1-86:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{ball_et_al:LIPIcs.ITCS.2020.86,
  author =	{Ball, Marshall and Holmgren, Justin and Ishai, Yuval and Liu, Tianren and Malkin, Tal},
  title =	{{On the Complexity of Decomposable Randomized Encodings, Or: How Friendly Can a Garbling-Friendly PRF Be?}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{86:1--86:22},
  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.2020.86},
  URN =		{urn:nbn:de:0030-drops-117714},
  doi =		{10.4230/LIPIcs.ITCS.2020.86},
  annote =	{Keywords: Randomized Encoding, Private Simultaneous Messages}
}
Document
Complete Volume
LIPIcs, Volume 32, SNAPL'15, Complete Volume

Authors: Thomas Ball, Rastislav Bodik, Shriram Krishnamurthi, Benjamin S. Lerner, and Greg Morrisett

Published in: LIPIcs, Volume 32, 1st Summit on Advances in Programming Languages (SNAPL 2015)


Abstract
LIPIcs, Volume 32, SNAPL'15, Complete Volume

Cite as

1st Summit on Advances in Programming Languages (SNAPL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 32, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@Proceedings{ball_et_al:LIPIcs.SNAPL.2015,
  title =	{{LIPIcs, Volume 32, SNAPL'15, Complete Volume}},
  booktitle =	{1st Summit on Advances in Programming Languages (SNAPL 2015)},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-80-4},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{32},
  editor =	{Ball, Thomas and Bodík, Rastislav and Krishnamurthi, Shriram and Lerner, Benjamin S. and Morriset, Greg},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SNAPL.2015},
  URN =		{urn:nbn:de:0030-drops-50461},
  doi =		{10.4230/LIPIcs.SNAPL.2015},
  annote =	{Keywords: Programming Languages}
}
Document
Front Matter
Title, Table of Contents, Preface, List of Authors

Authors: Thomas Ball, Rastislav Bodík, Shriram Krishnamurthi, Benjamin S. Lerner, and Greg Morriset

Published in: LIPIcs, Volume 32, 1st Summit on Advances in Programming Languages (SNAPL 2015)


Abstract
Title, Table of Contents, Preface, List of Authors

Cite as

1st Summit on Advances in Programming Languages (SNAPL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 32, pp. i-xiv, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{ball_et_al:LIPIcs.SNAPL.2015.i,
  author =	{Ball, Thomas and Bodík, Rastislav and Krishnamurthi, Shriram and Lerner, Benjamin S. and Morriset, Greg},
  title =	{{Title, Table of Contents, Preface, List of Authors}},
  booktitle =	{1st Summit on Advances in Programming Languages (SNAPL 2015)},
  pages =	{i--xiv},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-80-4},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{32},
  editor =	{Ball, Thomas and Bodík, Rastislav and Krishnamurthi, Shriram and Lerner, Benjamin S. and Morriset, Greg},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SNAPL.2015.i},
  URN =		{urn:nbn:de:0030-drops-50119},
  doi =		{10.4230/LIPIcs.SNAPL.2015.i},
  annote =	{Keywords: Title, Table of Contents, Preface, List of Authors}
}
Document
Coupling Memory and Computation for Locality Management

Authors: Umut A. Acar, Guy Blelloch, Matthew Fluet, Stefan K. Muller, and Ram Raghunathan

Published in: LIPIcs, Volume 32, 1st Summit on Advances in Programming Languages (SNAPL 2015)


Abstract
We articulate the need for managing (data) locality automatically rather than leaving it to the programmer, especially in parallel programming systems. To this end, we propose techniques for coupling tightly the computation (including the thread scheduler) and the memory manager so that data and computation can be positioned closely in hardware. Such tight coupling of computation and memory management is in sharp contrast with the prevailing practice of considering each in isolation. For example, memory-management techniques usually abstract the computation as an unknown "mutator", which is treated as a "black box". As an example of the approach, in this paper we consider a specific class of parallel computations, nested-parallel computations. Such computations dynamically create a nesting of parallel tasks. We propose a method for organizing memory as a tree of heaps reflecting the structure of the nesting. More specifically, our approach creates a heap for a task if it is separately scheduled on a processor. This allows us to couple garbage collection with the structure of the computation and the way in which it is dynamically scheduled on the processors. This coupling enables taking advantage of locality in the program by mapping it to the locality of the hardware. For example for improved locality a heap can be garbage collected immediately after its task finishes when the heap contents is likely in cache.

Cite as

Umut A. Acar, Guy Blelloch, Matthew Fluet, Stefan K. Muller, and Ram Raghunathan. Coupling Memory and Computation for Locality Management. In 1st Summit on Advances in Programming Languages (SNAPL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 32, pp. 1-14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{acar_et_al:LIPIcs.SNAPL.2015.1,
  author =	{Acar, Umut A. and Blelloch, Guy and Fluet, Matthew and Muller, Stefan K. and Raghunathan, Ram},
  title =	{{Coupling Memory and Computation for Locality Management}},
  booktitle =	{1st Summit on Advances in Programming Languages (SNAPL 2015)},
  pages =	{1--14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-80-4},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{32},
  editor =	{Ball, Thomas and Bodík, Rastislav and Krishnamurthi, Shriram and Lerner, Benjamin S. and Morriset, Greg},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SNAPL.2015.1},
  URN =		{urn:nbn:de:0030-drops-50121},
  doi =		{10.4230/LIPIcs.SNAPL.2015.1},
  annote =	{Keywords: Parallel computing, locality, memory management, parallel garbage collection, functional programming, nested parallelism, thread scheduling}
}
Document
Verified Compilers for a Multi-Language World

Authors: Amal Ahmed

Published in: LIPIcs, Volume 32, 1st Summit on Advances in Programming Languages (SNAPL 2015)


Abstract
Though there has been remarkable progress on formally verified compilers in recent years, most of these compilers suffer from a serious limitation: they are proved correct under the assumption that they will only be used to compile whole programs. This is an unrealistic assumption since most software systems today are comprised of components written in different languages - both typed and untyped - compiled by different compilers to a common target, as well as low-level libraries that may be handwritten in the target language. We are pursuing a new methodology for building verified compilers for today's world of multi-language software. The project has two central themes, both of which stem from a view of compiler correctness as a language interoperability problem. First, to specify correctness of component compilation, we require that if a source component s compiles to target component t, then t linked with some arbitrary target code t' should behave the same as s interoperating with t'. The latter demands a formal semantics of interoperability between the source and target languages. Second, to enable safe interoperability between components compiled from languages as different as ML, Rust, Python, and C, we plan to design a gradually type-safe target language based on LLVM that supports safe interoperability between more precisely typed, less precisely typed, and type-unsafe components. Our approach opens up a new avenue for exploring sensible language interoperability while also tackling compiler correctness.

Cite as

Amal Ahmed. Verified Compilers for a Multi-Language World. In 1st Summit on Advances in Programming Languages (SNAPL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 32, pp. 15-31, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{ahmed:LIPIcs.SNAPL.2015.15,
  author =	{Ahmed, Amal},
  title =	{{Verified Compilers for a Multi-Language World}},
  booktitle =	{1st Summit on Advances in Programming Languages (SNAPL 2015)},
  pages =	{15--31},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-80-4},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{32},
  editor =	{Ball, Thomas and Bodík, Rastislav and Krishnamurthi, Shriram and Lerner, Benjamin S. and Morriset, Greg},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SNAPL.2015.15},
  URN =		{urn:nbn:de:0030-drops-50131},
  doi =		{10.4230/LIPIcs.SNAPL.2015.15},
  annote =	{Keywords: verified compilation, compositional compiler correctness, multi-language semantics, typed low-level languages, gradual typing}
}
Document
Growing a Software Language for Hardware Design

Authors: Joshua Auerbach, David F. Bacon, Perry Cheng, Stephen J. Fink, Rodric Rabbah, and Sunil Shukla

Published in: LIPIcs, Volume 32, 1st Summit on Advances in Programming Languages (SNAPL 2015)


Abstract
The Liquid Metal project at IBM Research aimed to design and implement a new programming language called Lime to address some of the challenges posed by heterogeneous systems. Lime is a Java-compatible programming language with features designed to facilitate high level synthesis to hardware (FPGAs). This article reviews the language design from the outset, and highlights some of the earliest design decisions. We also describe how these decisions were revised recently to accommodate important requirements that arise in networking and cryptography.

Cite as

Joshua Auerbach, David F. Bacon, Perry Cheng, Stephen J. Fink, Rodric Rabbah, and Sunil Shukla. Growing a Software Language for Hardware Design. In 1st Summit on Advances in Programming Languages (SNAPL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 32, pp. 32-40, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{auerbach_et_al:LIPIcs.SNAPL.2015.32,
  author =	{Auerbach, Joshua and Bacon, David F. and Cheng, Perry and Fink, Stephen J. and Rabbah, Rodric and Shukla, Sunil},
  title =	{{Growing a Software Language for Hardware Design}},
  booktitle =	{1st Summit on Advances in Programming Languages (SNAPL 2015)},
  pages =	{32--40},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-80-4},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{32},
  editor =	{Ball, Thomas and Bodík, Rastislav and Krishnamurthi, Shriram and Lerner, Benjamin S. and Morriset, Greg},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SNAPL.2015.32},
  URN =		{urn:nbn:de:0030-drops-50144},
  doi =		{10.4230/LIPIcs.SNAPL.2015.32},
  annote =	{Keywords: Heterogeneous Systems, FPGA, High Level Synthesis, Dataflow, Functional Programming, Streaming, Java}
}
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