6 Search Results for "Parnas, David"


Document
On Property Testing of the Binary Rank

Authors: Nader H. Bshouty

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)


Abstract
Let M be an n × m (0,1)-matrix. We define the s-binary rank, denoted as br_s(M), of M as the minimum integer d such that there exist d monochromatic rectangles covering all the 1-entries in the matrix, with each 1-entry being covered by at most s rectangles. When s = 1, this corresponds to the binary rank, denoted as br(M), which is well-known in the literature and has many applications. Let R(M) and C(M) denote the sets of rows and columns of M, respectively. Using the result of Sgall [Jiří Sgall, 1999], we establish that if M has an s-binary rank at most d, then |R(M)| ⋅ |C(M)| ≤ binom(d, ≤ s)2^d, where binom(d, ≤ s) = ∑_{i=0}^s binom(d,i). This bound is tight, meaning that there exists a matrix M' with an s-binary rank of d, for which |R(M')| ⋅ |C(M')| = binom(d, ≤ s)2^d. Using this result, we present novel one-sided adaptive and non-adaptive testers for (0,1)-matrices with an s-binary rank at most d (and exactly d). These testers require Õ(binom(d, ≤ s)2^d/ε) and Õ(binom(d, ≤ s)2^d/ε²) queries, respectively. For a fixed s, this improves upon the query complexity of the tester proposed by Parnas et al. in [Michal Parnas et al., 2021] by a factor of Θ(2^d).

Cite as

Nader H. Bshouty. On Property Testing of the Binary Rank. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 27:1-27:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{bshouty:LIPIcs.MFCS.2023.27,
  author =	{Bshouty, Nader H.},
  title =	{{On Property Testing of the Binary Rank}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{27:1--27:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.27},
  URN =		{urn:nbn:de:0030-drops-185616},
  doi =		{10.4230/LIPIcs.MFCS.2023.27},
  annote =	{Keywords: Property testing, binary rank, Boolean rank}
}
Document
On the Binary and Boolean Rank of Regular Matrices

Authors: Ishay Haviv and Michal Parnas

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)


Abstract
A 0,1 matrix is said to be regular if all of its rows and columns have the same number of ones. We prove that for infinitely many integers k, there exists a square regular 0,1 matrix with binary rank k, such that the Boolean rank of its complement is k^Ω̃(log k). Equivalently, the ones in the matrix can be partitioned into k combinatorial rectangles, whereas the number of rectangles needed for any cover of its zeros is k^Ω̃(log k). This settles, in a strong form, a question of Pullman (Linear Algebra Appl., 1988) and a conjecture of Hefner, Henson, Lundgren, and Maybee (Congr. Numer., 1990). The result can be viewed as a regular analogue of a recent result of Balodis, Ben-David, Göös, Jain, and Kothari (FOCS, 2021), motivated by the clique vs. independent set problem in communication complexity and by the (disproved) Alon-Saks-Seymour conjecture in graph theory. As an application of the produced regular matrices, we obtain regular counterexamples to the Alon-Saks-Seymour conjecture and prove that for infinitely many integers k, there exists a regular graph with biclique partition number k and chromatic number k^Ω̃(log k).

Cite as

Ishay Haviv and Michal Parnas. On the Binary and Boolean Rank of Regular Matrices. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 56:1-56:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{haviv_et_al:LIPIcs.MFCS.2022.56,
  author =	{Haviv, Ishay and Parnas, Michal},
  title =	{{On the Binary and Boolean Rank of Regular Matrices}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{56:1--56:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.56},
  URN =		{urn:nbn:de:0030-drops-168545},
  doi =		{10.4230/LIPIcs.MFCS.2022.56},
  annote =	{Keywords: Binary rank, Boolean rank, Regular matrices, Non-deterministic communication complexity, Biclique partition number, Chromatic number}
}
Document
Flipping out with Many Flips: Hardness of Testing k-Monotonicity

Authors: Elena Grigorescu, Akash Kumar, and Karl Wimmer

Published in: LIPIcs, Volume 116, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)


Abstract
A function f:{0,1}^n - > {0,1} is said to be k-monotone if it flips between 0 and 1 at most k times on every ascending chain. Such functions represent a natural generalization of (1-)monotone functions, and have been recently studied in circuit complexity, PAC learning, and cryptography. Our work is part of a renewed focus in understanding testability of properties characterized by freeness of arbitrary order patterns as a generalization of monotonicity. Recently, Canonne et al. (ITCS 2017) initiate the study of k-monotone functions in the area of property testing, and Newman et al. (SODA 2017) study testability of families characterized by freeness from order patterns on real-valued functions over the line [n] domain. We study k-monotone functions in the more relaxed parametrized property testing model, introduced by Parnas et al. (JCSS, 72(6), 2006). In this process we resolve a problem left open in previous work. Specifically, our results include the following. 1) Testing 2-monotonicity on the hypercube non-adaptively with one-sided error requires an exponential in sqrt{n} number of queries. This behavior shows a stark contrast with testing (1-)monotonicity, which only needs O~(sqrt{n}) queries (Khot et al. (FOCS 2015)). Furthermore, even the apparently easier task of distinguishing 2-monotone functions from functions that are far from being n^{.01}-monotone also requires an exponential number of queries. 2) On the hypercube [n]^d domain, there exists a testing algorithm that makes a constant number of queries and distinguishes functions that are k-monotone from functions that are far from being O(kd^2) -monotone. Such a dependency is likely necessary, given the lower bound above for the hypercube.

Cite as

Elena Grigorescu, Akash Kumar, and Karl Wimmer. Flipping out with Many Flips: Hardness of Testing k-Monotonicity. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 40:1-40:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{grigorescu_et_al:LIPIcs.APPROX-RANDOM.2018.40,
  author =	{Grigorescu, Elena and Kumar, Akash and Wimmer, Karl},
  title =	{{Flipping out with Many Flips: Hardness of Testing k-Monotonicity}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{40:1--40:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-085-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{116},
  editor =	{Blais, Eric and Jansen, Klaus and D. P. Rolim, Jos\'{e} and Steurer, David},
  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.2018.40},
  URN =		{urn:nbn:de:0030-drops-94448},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.40},
  annote =	{Keywords: Property Testing, Boolean Functions, k-Monotonicity, Lower Bounds}
}
Document
Supporting Customer-Supplier Relationships: Requirements Engineering and Quality Assurance (Dagstuhl Seminar 02361)

Authors: Barbara Paech, David Parnas, Jesse H. Poore, H. Dieter Rombach, and Rudolf van Megen

Published in: Dagstuhl Seminar Reports. Dagstuhl Seminar Reports, Volume 1 (2021)


Abstract

Cite as

Barbara Paech, David Parnas, Jesse H. Poore, H. Dieter Rombach, and Rudolf van Megen. Supporting Customer-Supplier Relationships: Requirements Engineering and Quality Assurance (Dagstuhl Seminar 02361). Dagstuhl Seminar Report 352, pp. 1-22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2002)


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@TechReport{paech_et_al:DagSemRep.352,
  author =	{Paech, Barbara and Parnas, David and Poore, Jesse H. and Rombach, H. Dieter and van Megen, Rudolf},
  title =	{{Supporting Customer-Supplier Relationships: Requirements Engineering and Quality Assurance (Dagstuhl Seminar 02361)}},
  pages =	{1--22},
  ISSN =	{1619-0203},
  year =	{2002},
  type = 	{Dagstuhl Seminar Report},
  number =	{352},
  institution =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemRep.352},
  URN =		{urn:nbn:de:0030-drops-152320},
  doi =		{10.4230/DagSemRep.352},
}
Document
Software Engineering Research and Education: Seeking a new Agenda (Dagstuhl Seminar 99071)

Authors: Ernst Denert, Daniel Hoffman, Jochen Ludewig, and David L. Parnas

Published in: Dagstuhl Seminar Reports. Dagstuhl Seminar Reports, Volume 1 (2021)


Abstract

Cite as

Ernst Denert, Daniel Hoffman, Jochen Ludewig, and David L. Parnas. Software Engineering Research and Education: Seeking a new Agenda (Dagstuhl Seminar 99071). Dagstuhl Seminar Report 230, pp. 1-56, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (1999)


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@TechReport{denert_et_al:DagSemRep.230,
  author =	{Denert, Ernst and Hoffman, Daniel and Ludewig, Jochen and Parnas, David L.},
  title =	{{Software Engineering Research and Education: Seeking a new Agenda (Dagstuhl Seminar 99071)}},
  pages =	{1--56},
  ISSN =	{1619-0203},
  year =	{1999},
  type = 	{Dagstuhl Seminar Report},
  number =	{230},
  institution =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemRep.230},
  URN =		{urn:nbn:de:0030-drops-151162},
  doi =		{10.4230/DagSemRep.230},
}
Document
Requirements Capture, Documentation and Validation (Dagstuhl Seminar 99241)

Authors: Egon Börger, Bärbeö Hörger, David Parnas, and Dieter Rombach

Published in: Dagstuhl Seminar Reports. Dagstuhl Seminar Reports, Volume 1 (2021)


Abstract

Cite as

Egon Börger, Bärbeö Hörger, David Parnas, and Dieter Rombach. Requirements Capture, Documentation and Validation (Dagstuhl Seminar 99241). Dagstuhl Seminar Report 242, pp. 1-31, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (1999)


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@TechReport{borger_et_al:DagSemRep.242,
  author =	{B\"{o}rger, Egon and H\"{o}rger, B\"{a}rbe\"{o} and Parnas, David and Rombach, Dieter},
  title =	{{Requirements Capture, Documentation and Validation (Dagstuhl Seminar 99241)}},
  pages =	{1--31},
  ISSN =	{1619-0203},
  year =	{1999},
  type = 	{Dagstuhl Seminar Report},
  number =	{242},
  institution =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemRep.242},
  URN =		{urn:nbn:de:0030-drops-151287},
  doi =		{10.4230/DagSemRep.242},
}
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