4 Search Results for "Barnat, Jiri"

Document
DOI: 10.4230/LIPIcs.STACS.2026.30
Spectral Norm, Economical Sieve, and Linear Invariance Testing of Boolean Functions

Authors: Swarnalipa Datta, Arijit Ghosh, Chandrima Kayal, Manaswi Paraashar, and Manmatha Roy

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
Given Boolean functions f, g : 𝔽₂ⁿ → {-1,+1}, we say they are linearly isomorphic if there exists A ∈ GL_n(𝔽₂) such that f(x) = g(Ax) for all x. We study this problem in the tolerant property testing framework under the known-unknown model, where g is given explicitly and f is accessible only via oracle queries, meaning the algorithm may adaptively request the value of f(x) for inputs x ∈ 𝔽₂ⁿ of its choice. Given parameters ε ≥ 0 and ω > 0, the goal is to distinguish whether there exists A ∈ GL_n(𝔽₂) such that the normalized Hamming distance between f and g(Ax) is at most ε, or whether for every A ∈ GL_n(𝔽₂) the distance is at least ε+ω. Our main result is a tolerant tester making Õ ((m/ω) ⁴) queries to f, where m is an upper bound on the spectral norm of g, improving the previous Õ ((m/ω) ^{24}) bound of Wimmer and Yoshida. We complement this with a nearly matching lower bound of Ω(m²) for constant ω (for example, ω = 1/4), improving the prior Ω(log m) lower bound of Grigorescu, Wimmer and Xie. A key technical ingredient on the algorithmic side is a query-efficient local list corrector. For the lower bound, we give a reduction from communication complexity using a novel subclass of Maiorana-McFarland functions from symmetric-key cryptography.
Cite as

Swarnalipa Datta, Arijit Ghosh, Chandrima Kayal, Manaswi Paraashar, and Manmatha Roy. Spectral Norm, Economical Sieve, and Linear Invariance Testing of Boolean Functions. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 30:1-30:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{datta_et_al:LIPIcs.STACS.2026.30,
  author =	{Datta, Swarnalipa and Ghosh, Arijit and Kayal, Chandrima and Paraashar, Manaswi and Roy, Manmatha},
  title =	{{Spectral Norm, Economical Sieve, and Linear Invariance Testing of Boolean Functions}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{30:1--30:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.30},
  URN =		{urn:nbn:de:0030-drops-255194},
  doi =		{10.4230/LIPIcs.STACS.2026.30},
  annote =	{Keywords: Boolean Function, Isomorphism of Boolean Function, Fourier Analysis, Sublinear Algorithm, Property Testing}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.66
Testing Isomorphism of Boolean Functions over Finite Abelian Groups

Authors: Swarnalipa Datta, Arijit Ghosh, Chandrima Kayal, Manaswi Paraashar, and Manmatha Roy

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

Abstract
Let f and g be Boolean functions over a finite Abelian group 𝒢, where g is fully known and f is accessible via queries; that is, given any x ∈ 𝒢, we can obtain the value f(x). We study the problem of tolerant isomorphism testing: given parameters ε ≥ 0 and τ > 0, the goal is to determine, using as few queries as possible, whether there exists an automorphism σ of 𝒢 such that the fractional Hamming distance between f∘σ and g is at most ε, or whether for every automorphism σ, the distance is at least ε + τ. We design an efficient tolerant property testing algorithm for this problem over finite Abelian groups with constant exponent. The exponent of a finite group refers to the largest order of any element in the group. The query complexity of our algorithm is polynomial in s and 1/τ, where s bounds the spectral norm of the function g, and τ is the tolerance parameter. In addition, we present an improved algorithm in the case where g is Fourier sparse, meaning that its Fourier expansion contains only a small number of nonzero coefficients. Our approach draws on key ideas from Abelian group theory and Fourier analysis, including the annihilator of a subgroup, Pontryagin duality, and a pseudo inner product defined over finite Abelian groups. We believe that these techniques will be useful more broadly in the design of property testing algorithms.
Cite as

Swarnalipa Datta, Arijit Ghosh, Chandrima Kayal, Manaswi Paraashar, and Manmatha Roy. Testing Isomorphism of Boolean Functions over Finite Abelian Groups. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 66:1-66:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{datta_et_al:LIPIcs.APPROX/RANDOM.2025.66,
  author =	{Datta, Swarnalipa and Ghosh, Arijit and Kayal, Chandrima and Paraashar, Manaswi and Roy, Manmatha},
  title =	{{Testing Isomorphism of Boolean Functions over Finite Abelian Groups}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{66:1--66:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.66},
  URN =		{urn:nbn:de:0030-drops-244328},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.66},
  annote =	{Keywords: Analysis of Boolean functions, Abelian groups, Automorphism group, Function isomorphism, Spectral norm}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2016.50
Tunable Online MUS/MSS Enumeration

Authors: Jaroslav Bendík, Nikola Benes, Ivana Cerná, and Jirí Barnat

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

Abstract
In various areas of computer science, the problem of dealing with a set of constraints arises. If the set of constraints is unsatisfiable, one may ask for a minimal description of the reason for this unsatisifiability. Minimal unsatisfiable subsets (MUSes) and maximal satisfiable subsets (MSSes) are two kinds of such minimal descriptions. The goal of this work is the enumeration of MUSes and MSSes for a given constraint system. As such full enumeration may be intractable in general, we focus on building an online algorithm, which produces MUSes/MSSes in an on-the-fly manner as soon as they are discovered. The problem has been studied before even in its online version. However, our algorithm uses a novel approach that is able to outperform the current state-of-the art algorithms for online MUS/MSS enumeration. Moreover, the performance of our algorithm can be adjusted using tunable parameters. We evaluate the algorithm on a set of benchmarks.
Cite as

Jaroslav Bendík, Nikola Benes, Ivana Cerná, and Jirí Barnat. Tunable Online MUS/MSS Enumeration. 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. 50:1-50:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

Copy BibTex To Clipboard

@InProceedings{bendik_et_al:LIPIcs.FSTTCS.2016.50,
  author =	{Bend{\'\i}k, Jaroslav and Benes, Nikola and Cern\'{a}, Ivana and Barnat, Jir{\'\i}},
  title =	{{Tunable Online MUS/MSS Enumeration}},
  booktitle =	{36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)},
  pages =	{50:1--50:13},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2016.50},
  URN =		{urn:nbn:de:0030-drops-68855},
  doi =		{10.4230/LIPIcs.FSTTCS.2016.50},
  annote =	{Keywords: Minimal unsatisfiable subsets, Maximal satisfiable subsets, Unsatisfiab- ility analysis, Infeasibility analysis}
}
Document
DOI: 10.4230/DagSemProc.08332.4
Efficient Large-Scale Model Checking

Authors: Kees Verstoep, Henri E. Bal, Jiri Barnat, and Lubos Brim

Published in: Dagstuhl Seminar Proceedings, Volume 8332, Distributed Verification and Grid Computing (2008)

Abstract
Model checking is a popular technique to systematically and automatically verify system properties. Unfortunately, the well-known state explosion problem often limits the extent to which it can be applied to realistic specifications, due to the huge resulting memory requirements. Distributed memory model checkers exist, but have thus far only been evaluated on small-scale clusters, with mixed results. We examine one well-known distributed model checker in detail, and show how a number of additional optimizations in its runtime system enable it to efficiently check very demanding problem instances on a large-scale, multi-core compute cluster. We analyze the impact of the distributed algorithms employed, the problem instance characteristics and network overhead. Finally, we show that the model checker can even obtain good performance in a high-bandwidth computational grid environment.
Cite as

Kees Verstoep, Henri E. Bal, Jiri Barnat, and Lubos Brim. Efficient Large-Scale Model Checking. In Distributed Verification and Grid Computing. Dagstuhl Seminar Proceedings, Volume 8332, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

Copy BibTex To Clipboard

@InProceedings{verstoep_et_al:DagSemProc.08332.4,
  author =	{Verstoep, Kees and Bal, Henri E. and Barnat, Jiri and Brim, Lubos},
  title =	{{Efficient Large-Scale Model Checking}},
  booktitle =	{Distributed Verification and Grid Computing},
  pages =	{1--15},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8332},
  editor =	{Henri E. Bal and Lubos Brim and Martin Leucker},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08332.4},
  URN =		{urn:nbn:de:0030-drops-16309},
  doi =		{10.4230/DagSemProc.08332.4},
  annote =	{Keywords: Distributed model checking, Grid-based model checking}
}
  • Refine by Type
  • 4 Document/PDF
  • 2 Document/HTML

  • Refine by Publication Year
  • 1 2026
  • 1 2025
  • 1 2016
  • 1 2008

  • Refine by Author
  • 2 Datta, Swarnalipa
  • 2 Ghosh, Arijit
  • 2 Kayal, Chandrima
  • 2 Paraashar, Manaswi
  • 2 Roy, Manmatha
  • Show More...

  • Refine by Series/Journal
  • 3 LIPIcs
  • 1 DagSemProc

  • Refine by Classification
  • 2 Theory of computation → Boolean function learning

  • Refine by Keyword
  • 1 Abelian groups
  • 1 Analysis of Boolean functions
  • 1 Automorphism group
  • 1 Boolean Function
  • 1 Distributed model checking
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact