6 Search Results for "Dinesh, Krishnamoorthy"


Document
Bounded Simultaneous Messages

Authors: Andrej Bogdanov, Krishnamoorthy Dinesh, Yuval Filmus, Yuval Ishai, Avi Kaplan, and Sruthi Sekar

Published in: LIPIcs, Volume 284, 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)


Abstract
We consider the following question of bounded simultaneous messages (BSM) protocols: Can computationally unbounded Alice and Bob evaluate a function f(x,y) of their inputs by sending polynomial-size messages to a computationally bounded Carol? The special case where f is the mod-2 inner-product function and Carol is bounded to AC⁰ has been studied in previous works. The general question can be broadly motivated by applications in which distributed computation is more costly than local computation. In this work, we initiate a more systematic study of the BSM model, with different functions f and computational bounds on Carol. In particular, we give evidence against the existence of BSM protocols with polynomial-size Carol for naturally distributed variants of NP-complete languages.

Cite as

Andrej Bogdanov, Krishnamoorthy Dinesh, Yuval Filmus, Yuval Ishai, Avi Kaplan, and Sruthi Sekar. Bounded Simultaneous Messages. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 23:1-23:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{bogdanov_et_al:LIPIcs.FSTTCS.2023.23,
  author =	{Bogdanov, Andrej and Dinesh, Krishnamoorthy and Filmus, Yuval and Ishai, Yuval and Kaplan, Avi and Sekar, Sruthi},
  title =	{{Bounded Simultaneous Messages}},
  booktitle =	{43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)},
  pages =	{23:1--23:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-304-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{284},
  editor =	{Bouyer, Patricia and Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2023.23},
  URN =		{urn:nbn:de:0030-drops-193961},
  doi =		{10.4230/LIPIcs.FSTTCS.2023.23},
  annote =	{Keywords: Simultaneous Messages, Instance Hiding, Algebraic degree, Preprocessing, Lower Bounds}
}
Document
RANDOM
Classical Simulation of One-Query Quantum Distinguishers

Authors: Andrej Bogdanov, Tsun Ming Cheung, Krishnamoorthy Dinesh, and John C. S. Lui

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


Abstract
We study the relative advantage of classical and quantum distinguishers of bounded query complexity over n-bit strings, focusing on the case of a single quantum query. A construction of Aaronson and Ambainis (STOC 2015) yields a pair of distributions that is ε-distinguishable by a one-query quantum algorithm, but O(ε k/√n)-indistinguishable by any non-adaptive k-query classical algorithm. We show that every pair of distributions that is ε-distinguishable by a one-query quantum algorithm is distinguishable with k classical queries and (1) advantage min{Ω(ε√{k/n})), Ω(ε²k²/n)} non-adaptively (i.e., in one round), and (2) advantage Ω(ε²k/√{n log n}) in two rounds. As part of our analysis, we introduce a general method for converting unbiased estimators into distinguishers.

Cite as

Andrej Bogdanov, Tsun Ming Cheung, Krishnamoorthy Dinesh, and John C. S. Lui. Classical Simulation of One-Query Quantum Distinguishers. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 43:1-43:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{bogdanov_et_al:LIPIcs.APPROX/RANDOM.2023.43,
  author =	{Bogdanov, Andrej and Cheung, Tsun Ming and Dinesh, Krishnamoorthy and Lui, John C. S.},
  title =	{{Classical Simulation of One-Query Quantum Distinguishers}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{43:1--43:17},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.43},
  URN =		{urn:nbn:de:0030-drops-188684},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.43},
  annote =	{Keywords: Query complexity, quantum algorithms, hypothesis testing, Grothendieck’s inequality}
}
Document
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-dev.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}
}
Document
Diameter Versus Certificate Complexity of Boolean Functions

Authors: Siddhesh Chaubal and Anna Gál

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)


Abstract
In this paper, we introduce a measure of Boolean functions we call diameter, that captures the relationship between certificate complexity and several other measures of Boolean functions. Our measure can be viewed as a variation on alternating number, but while alternating number can be exponentially larger than certificate complexity, we show that diameter is always upper bounded by certificate complexity. We argue that estimating diameter may help to get improved bounds on certificate complexity in terms of sensitivity, and other measures. Previous results due to Lin and Zhang [Krishnamoorthy Dinesh and Jayalal Sarma, 2018] imply that s(f) ≥ Ω(n^{1/3}) for transitive functions with constant alternating number. We improve and extend this bound and prove that s(f) ≥ √n for transitive functions with constant alternating number, as well as for transitive functions with constant diameter. {We also show that bs(f) ≥ Ω(n^{3/7}) for transitive functions under the weaker condition that the "minimum" diameter is constant.} Furthermore, we prove that the log-rank conjecture holds for functions of the form f(x ⊕ y) for functions f with diameter bounded above by a polynomial of the logarithm of the Fourier sparsity of the function f.

Cite as

Siddhesh Chaubal and Anna Gál. Diameter Versus Certificate Complexity of Boolean Functions. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 31:1-31:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{chaubal_et_al:LIPIcs.MFCS.2021.31,
  author =	{Chaubal, Siddhesh and G\'{a}l, Anna},
  title =	{{Diameter Versus Certificate Complexity of Boolean Functions}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{31:1--31:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.31},
  URN =		{urn:nbn:de:0030-drops-144713},
  doi =		{10.4230/LIPIcs.MFCS.2021.31},
  annote =	{Keywords: Sensitivity Conjecture, Boolean Functions, Certificate Complexity, Block Sensitivity, Log-rank Conjecture, Alternating Number}
}
Document
Limits of Preprocessing

Authors: Yuval Filmus, Yuval Ishai, Avi Kaplan, and Guy Kindler

Published in: LIPIcs, Volume 169, 35th Computational Complexity Conference (CCC 2020)


Abstract
It is a classical result that the inner product function cannot be computed by an AC⁰ circuit [Merrick L. Furst et al., 1981; Miklós Ajtai, 1983; Johan Håstad, 1986]. It is conjectured that this holds even if we allow arbitrary preprocessing of each of the two inputs separately. We prove this conjecture when the preprocessing of one of the inputs is limited to output n + n/(log^{ω(1)} n) bits. Our methods extend to many other functions, including pseudorandom functions, and imply a (weak but nontrivial) limitation on the power of encoding inputs in low-complexity cryptography. Finally, under cryptographic assumptions, we relate the question of proving variants of the main conjecture with the question of learning AC⁰ under simple input distributions.

Cite as

Yuval Filmus, Yuval Ishai, Avi Kaplan, and Guy Kindler. Limits of Preprocessing. In 35th Computational Complexity Conference (CCC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 169, pp. 17:1-17:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{filmus_et_al:LIPIcs.CCC.2020.17,
  author =	{Filmus, Yuval and Ishai, Yuval and Kaplan, Avi and Kindler, Guy},
  title =	{{Limits of Preprocessing}},
  booktitle =	{35th Computational Complexity Conference (CCC 2020)},
  pages =	{17:1--17:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-156-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{169},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2020.17},
  URN =		{urn:nbn:de:0030-drops-125697},
  doi =		{10.4230/LIPIcs.CCC.2020.17},
  annote =	{Keywords: circuit, communication complexity, IPPP, preprocessing, PRF, simultaneous messages}
}
Document
Characterization and Lower Bounds for Branching Program Size Using Projective Dimension

Authors: Krishnamoorthy Dinesh, Sajin Koroth, and Jayalal Sarma

Published in: LIPIcs, Volume 65, 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)


Abstract
We study projective dimension, a graph parameter (denoted by pd(G) for a graph G), introduced by Pudlak and Rodl (1992). For a Boolean function f(on n bits), Pudlak and Rodl associated a bipartite graph G_f and showed that size of the optimal branching program computing f (denoted by bpsize(f)) is at least pd(G_f) (also denoted by pd(f)). Hence, proving lower bounds for pd(f) imply lower bounds for bpsize(f). Despite several attempts (Pudlak and Rodl (1992), Ronyai et.al, (2000)), proving super-linear lower bounds for projective dimension of explicit families of graphs has remained elusive. We observe that there exist a Boolean function f for which the gap between the pd(f) and bpsize(f) is 2^{Omega(n)}. Motivated by the argument in Pudlak and Rodl (1992), we define two variants of projective dimension - projective dimension with intersection dimension 1 (denoted by upd(f)) and {bitwise decomposable projective dimension} (denoted by bpdim(f)). We show the following results: (a) We observe that there exist a Boolean function f for which the gap between upd(f) and bpsize(f) is 2^{Omega(n)}. In contrast, we also show that the bitwise decomposable projective dimension characterizes size of the branching program up to a polynomial factor. That is, there exists a large constant c>0 and for any function f, bpdim(f)/6 <= bpsize(f) <= (bpdim(f))^c. (b) We introduce a new candidate function family f for showing super-polynomial lower bounds for bpdim(f). As our main result, we demonstrate gaps between pd(f) and the above two new measures for f: pd(f) = O(sqrt{n}), upd(f) = Omega(n), bpdim(f) = Omega({n^{1.5}}/{log(n)}). (c) Although not related to branching program lower bounds, we derive exponential lower bounds for two restricted variants of pd(f) and upd(f) respectively by observing that they are exactly equal to well-studied graph parameters - bipartite clique cover number and bipartite partition number respectively.

Cite as

Krishnamoorthy Dinesh, Sajin Koroth, and Jayalal Sarma. Characterization and Lower Bounds for Branching Program Size Using Projective Dimension. In 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 65, pp. 37:1-37:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{dinesh_et_al:LIPIcs.FSTTCS.2016.37,
  author =	{Dinesh, Krishnamoorthy and Koroth, Sajin and Sarma, Jayalal},
  title =	{{Characterization and Lower Bounds for Branching Program Size Using Projective Dimension}},
  booktitle =	{36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)},
  pages =	{37:1--37:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-027-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{65},
  editor =	{Lal, Akash and Akshay, S. and Saurabh, Saket and Sen, Sandeep},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2016.37},
  URN =		{urn:nbn:de:0030-drops-68722},
  doi =		{10.4230/LIPIcs.FSTTCS.2016.37},
  annote =	{Keywords: Projective Dimension, Lower Bounds, Branching Program Size}
}
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