Complexity of some arithmetic problems for binary polynomials View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2003-06

AUTHORS

Eric Allender, Anna Bernasconi, Carsten Damm, Joachim von zur Gathen, Michael Saks, Igor Shparlinski

ABSTRACT

We study various combinatorial complexity measures of Boolean functions related to some natural arithmetic problems about binary polynomials, that is, polynomials over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathbb{F}_2 $$\end{document}. In particular, we consider the Boolean function deciding whether a given polynomial over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathbb{F}_2 $$\end{document} is squarefree. We obtain an exponential lower bound on the size of a decision tree for this function, and derive an asymptotic formula, having a linear main term, for its average sensitivity. This allows us to estimate other complexity characteristics such as the formula size, the average decision tree depth and the degrees of exact and approximative polynomial representations of this function. Finally, using a different method, we show that testing squarefreeness and irreducibility of polynomials over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathbb{F}_2 $$\end{document} cannot be done in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \textrm{AC}^0[p] $$\end{document} for any odd prime p. Similar results are obtained for deciding coprimality of two polynomials over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathbb{F}_2 $$\end{document} as well. More... »

PAGES

23-47

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00037-003-0176-9

DOI

http://dx.doi.org/10.1007/s00037-003-0176-9

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1036061354


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/08", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Information and Computing Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/17", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Psychology and Cognitive Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0801", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Artificial Intelligence and Image Processing", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0802", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Computation Theory and Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/1702", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Cognitive Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Department of Computer Science, Rutgers University, 08854-8019, Piscataway, NJ, USA", 
          "id": "http://www.grid.ac/institutes/grid.430387.b", 
          "name": [
            "Department of Computer Science, Rutgers University, 08854-8019, Piscataway, NJ, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Allender", 
        "givenName": "Eric", 
        "id": "sg:person.01074752454.82", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01074752454.82"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Dipartimento di Informatica, Universit\u00e0 di Pisa, 56127, Pisa, Italy", 
          "id": "http://www.grid.ac/institutes/grid.5395.a", 
          "name": [
            "Dipartimento di Informatica, Universit\u00e0 di Pisa, 56127, Pisa, Italy"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Bernasconi", 
        "givenName": "Anna", 
        "id": "sg:person.013333157113.36", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013333157113.36"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Institut f\u00fcr Numerische und Angewandte Mathematik, Universit\u00e4t G\u00f6ttingen, 37083, G\u00f6ttingen, Germany", 
          "id": "http://www.grid.ac/institutes/grid.7450.6", 
          "name": [
            "Institut f\u00fcr Numerische und Angewandte Mathematik, Universit\u00e4t G\u00f6ttingen, 37083, G\u00f6ttingen, Germany"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Damm", 
        "givenName": "Carsten", 
        "id": "sg:person.016125064101.54", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016125064101.54"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Fakult\u00e4t f\u00fcr Elektrotechnik, Informatik und Mathematik, Universit\u00e4t Paderborn, 33095, Paderborn, Germany", 
          "id": "http://www.grid.ac/institutes/grid.5659.f", 
          "name": [
            "Fakult\u00e4t f\u00fcr Elektrotechnik, Informatik und Mathematik, Universit\u00e4t Paderborn, 33095, Paderborn, Germany"
          ], 
          "type": "Organization"
        }, 
        "familyName": "von zur Gathen", 
        "givenName": "Joachim", 
        "id": "sg:person.013654024753.29", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013654024753.29"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Mathematics Department, Rutgers University, 08854-8019, Piscataway, NJ, USA", 
          "id": "http://www.grid.ac/institutes/grid.430387.b", 
          "name": [
            "Mathematics Department, Rutgers University, 08854-8019, Piscataway, NJ, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Saks", 
        "givenName": "Michael", 
        "id": "sg:person.011520224512.05", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011520224512.05"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Computing, Macquarie University, 2109, NSW, Australia", 
          "id": "http://www.grid.ac/institutes/grid.1004.5", 
          "name": [
            "Department of Computing, Macquarie University, 2109, NSW, Australia"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Shparlinski", 
        "givenName": "Igor", 
        "id": "sg:person.013727467104.70", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013727467104.70"
        ], 
        "type": "Person"
      }
    ], 
    "datePublished": "2003-06", 
    "datePublishedReg": "2003-06-01", 
    "description": "We study various combinatorial complexity measures of\nBoolean functions related to some natural arithmetic problems about\nbinary polynomials, that is, polynomials over \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$ \\mathbb{F}_2 $$\\end{document}. \nIn particular, we consider\nthe Boolean function deciding whether a given polynomial over \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$ \\mathbb{F}_2 $$\\end{document}\nis squarefree. We obtain an exponential lower bound on the size of a\ndecision tree for this function, and derive an asymptotic formula, having\na linear main term, for its average sensitivity. This allows us to estimate\nother complexity characteristics such as the formula size, the average decision\ntree depth and the degrees of exact and approximative polynomial\nrepresentations of this function. Finally, using a different method, we\nshow that testing squarefreeness and irreducibility of polynomials over\n\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$ \\mathbb{F}_2 $$\\end{document} cannot be done in \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$ \\textrm{AC}^0[p] $$\\end{document} \nfor any odd prime p. Similar results are\nobtained for deciding coprimality of two polynomials over \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$ \\mathbb{F}_2 $$\\end{document} as well.", 
    "genre": "article", 
    "id": "sg:pub.10.1007/s00037-003-0176-9", 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1136224", 
        "issn": [
          "1016-3328", 
          "1420-8954"
        ], 
        "name": "computational complexity", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1-2", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "12"
      }
    ], 
    "keywords": [
      "irreducibility of polynomials", 
      "odd prime p.", 
      "binary polynomials", 
      "asymptotic formula", 
      "combinatorial complexity measures", 
      "polynomials", 
      "Boolean functions", 
      "primes p.", 
      "complexity measures", 
      "main terms", 
      "formula size", 
      "complexity characteristics", 
      "arithmetic problems", 
      "problem", 
      "tree depth", 
      "irreducibility", 
      "coprimality", 
      "squarefreeness", 
      "function", 
      "different methods", 
      "squarefree", 
      "formula", 
      "average decision", 
      "representation", 
      "complexity", 
      "terms", 
      "decision tree", 
      "similar results", 
      "size", 
      "results", 
      "p.", 
      "trees", 
      "average sensitivity", 
      "degree", 
      "characteristics", 
      "measures", 
      "decisions", 
      "depth", 
      "sensitivity", 
      "method"
    ], 
    "name": "Complexity of some arithmetic problems for binary polynomials", 
    "pagination": "23-47", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1036061354"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s00037-003-0176-9"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s00037-003-0176-9", 
      "https://app.dimensions.ai/details/publication/pub.1036061354"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2022-09-02T15:49", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20220902/entities/gbq_results/article/article_363.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1007/s00037-003-0176-9"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s00037-003-0176-9'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s00037-003-0176-9'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00037-003-0176-9'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00037-003-0176-9'


 

This table displays all metadata directly associated to this object as RDF triples.

158 TRIPLES      20 PREDICATES      68 URIs      57 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s00037-003-0176-9 schema:about anzsrc-for:08
2 anzsrc-for:0801
3 anzsrc-for:0802
4 anzsrc-for:17
5 anzsrc-for:1702
6 schema:author N7da6a7ef2d4c492ea12ffd50e5eb69a4
7 schema:datePublished 2003-06
8 schema:datePublishedReg 2003-06-01
9 schema:description We study various combinatorial complexity measures of Boolean functions related to some natural arithmetic problems about binary polynomials, that is, polynomials over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathbb{F}_2 $$\end{document}. In particular, we consider the Boolean function deciding whether a given polynomial over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathbb{F}_2 $$\end{document} is squarefree. We obtain an exponential lower bound on the size of a decision tree for this function, and derive an asymptotic formula, having a linear main term, for its average sensitivity. This allows us to estimate other complexity characteristics such as the formula size, the average decision tree depth and the degrees of exact and approximative polynomial representations of this function. Finally, using a different method, we show that testing squarefreeness and irreducibility of polynomials over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathbb{F}_2 $$\end{document} cannot be done in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \textrm{AC}^0[p] $$\end{document} for any odd prime p. Similar results are obtained for deciding coprimality of two polynomials over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathbb{F}_2 $$\end{document} as well.
10 schema:genre article
11 schema:isAccessibleForFree false
12 schema:isPartOf N86f0e65a1d7e47aba2020746f611794c
13 Nf37acc1bea8141efb1a214c3fc12aea8
14 sg:journal.1136224
15 schema:keywords Boolean functions
16 arithmetic problems
17 asymptotic formula
18 average decision
19 average sensitivity
20 binary polynomials
21 characteristics
22 combinatorial complexity measures
23 complexity
24 complexity characteristics
25 complexity measures
26 coprimality
27 decision tree
28 decisions
29 degree
30 depth
31 different methods
32 formula
33 formula size
34 function
35 irreducibility
36 irreducibility of polynomials
37 main terms
38 measures
39 method
40 odd prime p.
41 p.
42 polynomials
43 primes p.
44 problem
45 representation
46 results
47 sensitivity
48 similar results
49 size
50 squarefree
51 squarefreeness
52 terms
53 tree depth
54 trees
55 schema:name Complexity of some arithmetic problems for binary polynomials
56 schema:pagination 23-47
57 schema:productId N1c9a992ed07d4e6d8df3d80a37dfa89a
58 N78ddfa9f8c534dc4aaeba6940d28fe49
59 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036061354
60 https://doi.org/10.1007/s00037-003-0176-9
61 schema:sdDatePublished 2022-09-02T15:49
62 schema:sdLicense https://scigraph.springernature.com/explorer/license/
63 schema:sdPublisher N8eafcfb052ed43ab9e244d1cb453f415
64 schema:url https://doi.org/10.1007/s00037-003-0176-9
65 sgo:license sg:explorer/license/
66 sgo:sdDataset articles
67 rdf:type schema:ScholarlyArticle
68 N1c9a992ed07d4e6d8df3d80a37dfa89a schema:name dimensions_id
69 schema:value pub.1036061354
70 rdf:type schema:PropertyValue
71 N3738be686ab74a2aaa93d69227b05270 rdf:first sg:person.011520224512.05
72 rdf:rest N67e452ac7b694c7c8ed20ec54a86c112
73 N50e349c5fdca4a8e9fdac3258a2a5d59 rdf:first sg:person.013654024753.29
74 rdf:rest N3738be686ab74a2aaa93d69227b05270
75 N67e452ac7b694c7c8ed20ec54a86c112 rdf:first sg:person.013727467104.70
76 rdf:rest rdf:nil
77 N78ddfa9f8c534dc4aaeba6940d28fe49 schema:name doi
78 schema:value 10.1007/s00037-003-0176-9
79 rdf:type schema:PropertyValue
80 N7da6a7ef2d4c492ea12ffd50e5eb69a4 rdf:first sg:person.01074752454.82
81 rdf:rest N9e1015208fe14bffb20037190bfdbd2f
82 N86f0e65a1d7e47aba2020746f611794c schema:volumeNumber 12
83 rdf:type schema:PublicationVolume
84 N8eafcfb052ed43ab9e244d1cb453f415 schema:name Springer Nature - SN SciGraph project
85 rdf:type schema:Organization
86 N9e1015208fe14bffb20037190bfdbd2f rdf:first sg:person.013333157113.36
87 rdf:rest Ne3f7f3032fa047f7838c168ea4426049
88 Ne3f7f3032fa047f7838c168ea4426049 rdf:first sg:person.016125064101.54
89 rdf:rest N50e349c5fdca4a8e9fdac3258a2a5d59
90 Nf37acc1bea8141efb1a214c3fc12aea8 schema:issueNumber 1-2
91 rdf:type schema:PublicationIssue
92 anzsrc-for:08 schema:inDefinedTermSet anzsrc-for:
93 schema:name Information and Computing Sciences
94 rdf:type schema:DefinedTerm
95 anzsrc-for:0801 schema:inDefinedTermSet anzsrc-for:
96 schema:name Artificial Intelligence and Image Processing
97 rdf:type schema:DefinedTerm
98 anzsrc-for:0802 schema:inDefinedTermSet anzsrc-for:
99 schema:name Computation Theory and Mathematics
100 rdf:type schema:DefinedTerm
101 anzsrc-for:17 schema:inDefinedTermSet anzsrc-for:
102 schema:name Psychology and Cognitive Sciences
103 rdf:type schema:DefinedTerm
104 anzsrc-for:1702 schema:inDefinedTermSet anzsrc-for:
105 schema:name Cognitive Sciences
106 rdf:type schema:DefinedTerm
107 sg:journal.1136224 schema:issn 1016-3328
108 1420-8954
109 schema:name computational complexity
110 schema:publisher Springer Nature
111 rdf:type schema:Periodical
112 sg:person.01074752454.82 schema:affiliation grid-institutes:grid.430387.b
113 schema:familyName Allender
114 schema:givenName Eric
115 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01074752454.82
116 rdf:type schema:Person
117 sg:person.011520224512.05 schema:affiliation grid-institutes:grid.430387.b
118 schema:familyName Saks
119 schema:givenName Michael
120 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011520224512.05
121 rdf:type schema:Person
122 sg:person.013333157113.36 schema:affiliation grid-institutes:grid.5395.a
123 schema:familyName Bernasconi
124 schema:givenName Anna
125 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013333157113.36
126 rdf:type schema:Person
127 sg:person.013654024753.29 schema:affiliation grid-institutes:grid.5659.f
128 schema:familyName von zur Gathen
129 schema:givenName Joachim
130 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013654024753.29
131 rdf:type schema:Person
132 sg:person.013727467104.70 schema:affiliation grid-institutes:grid.1004.5
133 schema:familyName Shparlinski
134 schema:givenName Igor
135 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013727467104.70
136 rdf:type schema:Person
137 sg:person.016125064101.54 schema:affiliation grid-institutes:grid.7450.6
138 schema:familyName Damm
139 schema:givenName Carsten
140 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016125064101.54
141 rdf:type schema:Person
142 grid-institutes:grid.1004.5 schema:alternateName Department of Computing, Macquarie University, 2109, NSW, Australia
143 schema:name Department of Computing, Macquarie University, 2109, NSW, Australia
144 rdf:type schema:Organization
145 grid-institutes:grid.430387.b schema:alternateName Department of Computer Science, Rutgers University, 08854-8019, Piscataway, NJ, USA
146 Mathematics Department, Rutgers University, 08854-8019, Piscataway, NJ, USA
147 schema:name Department of Computer Science, Rutgers University, 08854-8019, Piscataway, NJ, USA
148 Mathematics Department, Rutgers University, 08854-8019, Piscataway, NJ, USA
149 rdf:type schema:Organization
150 grid-institutes:grid.5395.a schema:alternateName Dipartimento di Informatica, Università di Pisa, 56127, Pisa, Italy
151 schema:name Dipartimento di Informatica, Università di Pisa, 56127, Pisa, Italy
152 rdf:type schema:Organization
153 grid-institutes:grid.5659.f schema:alternateName Fakultät für Elektrotechnik, Informatik und Mathematik, Universität Paderborn, 33095, Paderborn, Germany
154 schema:name Fakultät für Elektrotechnik, Informatik und Mathematik, Universität Paderborn, 33095, Paderborn, Germany
155 rdf:type schema:Organization
156 grid-institutes:grid.7450.6 schema:alternateName Institut für Numerische und Angewandte Mathematik, Universität Göttingen, 37083, Göttingen, Germany
157 schema:name Institut für Numerische und Angewandte Mathematik, Universität Göttingen, 37083, Göttingen, Germany
158 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...