Derandomized Constructions of k-Wise (Almost) Independent Permutations View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2008-12-25

AUTHORS

Eyal Kaplan, Moni Naor, Omer Reingold

ABSTRACT

Constructions of k-wise almost independent permutations have been receiving a growing amount of attention in recent years. However, unlike the case of k-wise independent functions, the size of previously constructed families of such permutations is far from optimal. This paper gives a new method for reducing the size of families given by previous constructions. Our method relies on pseudorandom generators for space-bounded computations. In fact, all we need is a generator, that produces “pseudorandom walks” on undirected graphs with a consistent labelling. One such generator is implied by Reingold’s log-space algorithm for undirected connectivity (Reingold/Reingold et al. in Proc. of the 37th/38th Annual Symposium on Theory of Computing, pp. 376–385/457–466, 2005/2006). We obtain families of k-wise almost independent permutations, with an optimal description length, up to a constant factor. More precisely, if the distance from uniform for any k tuple should be at most δ, then the size of the description of a permutation in the family is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$O(kn+\log \frac{1}{\delta})$\end{document} . More... »

PAGES

113-133

References to SciGraph publications

  • 2005. Derandomized Squaring of Graphs in APPROXIMATION, RANDOMIZATION AND COMBINATORIAL OPTIMIZATION. ALGORITHMS AND TECHNIQUES
  • 2004. Black-Box Composition Does Not Imply Adaptive Security in ADVANCES IN CRYPTOLOGY - EUROCRYPT 2004
  • 2003-05-13. The Security of Many-Round Luby-Rackoff Pseudo-Random Permutations in ADVANCES IN CRYPTOLOGY — EUROCRYPT 2003
  • 2004. Security of Random Feistel Schemes with 5 or More Rounds in ADVANCES IN CRYPTOLOGY – CRYPTO 2004
  • 2004. Simple Permutations Mix Well in AUTOMATA, LANGUAGES AND PROGRAMMING
  • 2004. Composition of Random Systems: When Two Weak Make One Strong in THEORY OF CRYPTOGRAPHY
  • 2005. Composition Does Not Imply Adaptive Security in ADVANCES IN CRYPTOLOGY – CRYPTO 2005
  • 2003-09. Pushing Dependent Data in Clients–Providers–Servers Systems in WIRELESS NETWORKS
  • 1998-02. Approximating Probability Distributions Using Small Sample Spaces in COMBINATORICA
  • 1999-01. On the Construction of Pseudorandom Permutations: Luby—Rackoff Revisited in JOURNAL OF CRYPTOLOGY
  • 1996. A Course in the Theory of Groups in NONE
  • 1992-12. Pseudorandom generators for space-bounded computation in COMBINATORICA
  • 2002-02-08. Ciphers with Arbitrary Finite Domains in TOPICS IN CRYPTOLOGY — CT-RSA 2002
  • 2003. Luby-Rackoff: 7 Rounds Are Enough for 2n(1 − ε) Security in ADVANCES IN CRYPTOLOGY - CRYPTO 2003
  • 2005. Derandomized Constructions of k-Wise (Almost) Independent Permutations in APPROXIMATION, RANDOMIZATION AND COMBINATORIAL OPTIMIZATION. ALGORITHMS AND TECHNIQUES
  • 2002-04-29. How to Fool an Unbounded Adversary with a Short Key in ADVANCES IN CRYPTOLOGY — EUROCRYPT 2002
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00453-008-9267-y

    DOI

    http://dx.doi.org/10.1007/s00453-008-9267-y

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1019520288


    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/2008/17", 
            "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/2008/1701", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Psychology", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Tel-Aviv University, Tel-Aviv, Israel", 
              "id": "http://www.grid.ac/institutes/grid.12136.37", 
              "name": [
                "Tel-Aviv University, Tel-Aviv, Israel"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Kaplan", 
            "givenName": "Eyal", 
            "id": "sg:person.016351357345.24", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016351357345.24"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, 76100, Rehovot, Israel", 
              "id": "http://www.grid.ac/institutes/grid.13992.30", 
              "name": [
                "Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, 76100, Rehovot, Israel"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Naor", 
            "givenName": "Moni", 
            "id": "sg:person.07776170271.83", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07776170271.83"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, 76100, Rehovot, Israel", 
              "id": "http://www.grid.ac/institutes/grid.13992.30", 
              "name": [
                "Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, 76100, Rehovot, Israel"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Reingold", 
            "givenName": "Omer", 
            "id": "sg:person.012547246003.78", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012547246003.78"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/978-1-4419-8594-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1008672834", 
              "https://doi.org/10.1007/978-1-4419-8594-1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/3-540-46035-7_9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1031230716", 
              "https://doi.org/10.1007/3-540-46035-7_9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/pl00003817", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1017452659", 
              "https://doi.org/10.1007/pl00003817"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/3-540-45760-7_9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1002956912", 
              "https://doi.org/10.1007/3-540-45760-7_9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/pl00009813", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1042491565", 
              "https://doi.org/10.1007/pl00009813"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-27836-8_65", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1045310101", 
              "https://doi.org/10.1007/978-3-540-27836-8_65"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-24676-3_12", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1046250308", 
              "https://doi.org/10.1007/978-3-540-24676-3_12"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/11538462_30", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1037921863", 
              "https://doi.org/10.1007/11538462_30"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-45146-4_30", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1034759171", 
              "https://doi.org/10.1007/978-3-540-45146-4_30"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/3-540-39200-9_34", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1018703004", 
              "https://doi.org/10.1007/3-540-39200-9_34"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/11535218_4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1028351668", 
              "https://doi.org/10.1007/11535218_4"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-28628-8_7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025082760", 
              "https://doi.org/10.1007/978-3-540-28628-8_7"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1023/a:1024632031440", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015226359", 
              "https://doi.org/10.1023/a:1024632031440"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/11538462_37", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047027068", 
              "https://doi.org/10.1007/11538462_37"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01305237", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019048384", 
              "https://doi.org/10.1007/bf01305237"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-24638-1_23", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047813557", 
              "https://doi.org/10.1007/978-3-540-24638-1_23"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2008-12-25", 
        "datePublishedReg": "2008-12-25", 
        "description": "Constructions of k-wise almost independent permutations have been receiving a growing amount of attention in recent years. However, unlike the case of k-wise independent functions, the size of previously constructed families of such permutations is far from optimal. This paper gives a new method for reducing the size of families given by previous constructions. Our method relies on pseudorandom generators for space-bounded computations. In fact, all we need is a generator, that produces \u201cpseudorandom walks\u201d on undirected graphs with a consistent labelling. One such generator is implied by Reingold\u2019s log-space algorithm for undirected connectivity (Reingold/Reingold et al. in Proc. of the 37th/38th Annual Symposium on Theory of Computing, pp.\u00a0376\u2013385/457\u2013466, 2005/2006). We obtain families of k-wise almost independent permutations, with an optimal description length, up to a constant factor. More precisely, if the distance from uniform for any k tuple should be at most \u03b4, then the size of the description of a permutation in the family is \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}$O(kn+\\log \\frac{1}{\\delta})$\\end{document}\n.", 
        "genre": "article", 
        "id": "sg:pub.10.1007/s00453-008-9267-y", 
        "inLanguage": "en", 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1047644", 
            "issn": [
              "0178-4617", 
              "1432-0541"
            ], 
            "name": "Algorithmica", 
            "publisher": "Springer Nature", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "1", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "55"
          }
        ], 
        "keywords": [
          "construction", 
          "amount of attention", 
          "family", 
          "size of family", 
          "space-bounded computation", 
          "log-space algorithm", 
          "description length", 
          "permutations", 
          "attention", 
          "recent years", 
          "years", 
          "independent functions", 
          "function", 
          "such permutations", 
          "paper", 
          "new method", 
          "previous constructions", 
          "pseudorandom generators", 
          "generator", 
          "computation", 
          "fact", 
          "pseudorandom", 
          "undirected graph", 
          "graph", 
          "consistent labeling", 
          "such generators", 
          "algorithm", 
          "undirected connectivity", 
          "constant factor", 
          "tuples", 
          "description", 
          "amount", 
          "cases", 
          "size", 
          "method", 
          "labeling", 
          "connectivity", 
          "length", 
          "factors", 
          "distance", 
          "uniform", 
          "independent permutations", 
          "wise independent functions", 
          "Reingold\u2019s log-space algorithm", 
          "optimal description length", 
          "wise independent permutations"
        ], 
        "name": "Derandomized Constructions of k-Wise (Almost) Independent Permutations", 
        "pagination": "113-133", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1019520288"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s00453-008-9267-y"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s00453-008-9267-y", 
          "https://app.dimensions.ai/details/publication/pub.1019520288"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2022-01-01T18:19", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-springernature-scigraph/baseset/20220101/entities/gbq_results/article/article_466.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.1007/s00453-008-9267-y"
      }
    ]
     

    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/s00453-008-9267-y'

    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/s00453-008-9267-y'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00453-008-9267-y'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00453-008-9267-y'


     

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

    185 TRIPLES      22 PREDICATES      87 URIs      63 LITERALS      6 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s00453-008-9267-y schema:about anzsrc-for:17
    2 anzsrc-for:1701
    3 schema:author Nc2fdd6d572fc44c5b78036e293a0ec7e
    4 schema:citation sg:pub.10.1007/11535218_4
    5 sg:pub.10.1007/11538462_30
    6 sg:pub.10.1007/11538462_37
    7 sg:pub.10.1007/3-540-39200-9_34
    8 sg:pub.10.1007/3-540-45760-7_9
    9 sg:pub.10.1007/3-540-46035-7_9
    10 sg:pub.10.1007/978-1-4419-8594-1
    11 sg:pub.10.1007/978-3-540-24638-1_23
    12 sg:pub.10.1007/978-3-540-24676-3_12
    13 sg:pub.10.1007/978-3-540-27836-8_65
    14 sg:pub.10.1007/978-3-540-28628-8_7
    15 sg:pub.10.1007/978-3-540-45146-4_30
    16 sg:pub.10.1007/bf01305237
    17 sg:pub.10.1007/pl00003817
    18 sg:pub.10.1007/pl00009813
    19 sg:pub.10.1023/a:1024632031440
    20 schema:datePublished 2008-12-25
    21 schema:datePublishedReg 2008-12-25
    22 schema:description Constructions of k-wise almost independent permutations have been receiving a growing amount of attention in recent years. However, unlike the case of k-wise independent functions, the size of previously constructed families of such permutations is far from optimal. This paper gives a new method for reducing the size of families given by previous constructions. Our method relies on pseudorandom generators for space-bounded computations. In fact, all we need is a generator, that produces “pseudorandom walks” on undirected graphs with a consistent labelling. One such generator is implied by Reingold’s log-space algorithm for undirected connectivity (Reingold/Reingold et al. in Proc. of the 37th/38th Annual Symposium on Theory of Computing, pp. 376–385/457–466, 2005/2006). We obtain families of k-wise almost independent permutations, with an optimal description length, up to a constant factor. More precisely, if the distance from uniform for any k tuple should be at most δ, then the size of the description of a permutation in the family is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$O(kn+\log \frac{1}{\delta})$\end{document} .
    23 schema:genre article
    24 schema:inLanguage en
    25 schema:isAccessibleForFree false
    26 schema:isPartOf N37425c5d25264778aa1c5c664ac36c7a
    27 N56f33d7ac8334e4bb1308818be8903ed
    28 sg:journal.1047644
    29 schema:keywords Reingold’s log-space algorithm
    30 algorithm
    31 amount
    32 amount of attention
    33 attention
    34 cases
    35 computation
    36 connectivity
    37 consistent labeling
    38 constant factor
    39 construction
    40 description
    41 description length
    42 distance
    43 fact
    44 factors
    45 family
    46 function
    47 generator
    48 graph
    49 independent functions
    50 independent permutations
    51 labeling
    52 length
    53 log-space algorithm
    54 method
    55 new method
    56 optimal description length
    57 paper
    58 permutations
    59 previous constructions
    60 pseudorandom
    61 pseudorandom generators
    62 recent years
    63 size
    64 size of family
    65 space-bounded computation
    66 such generators
    67 such permutations
    68 tuples
    69 undirected connectivity
    70 undirected graph
    71 uniform
    72 wise independent functions
    73 wise independent permutations
    74 years
    75 schema:name Derandomized Constructions of k-Wise (Almost) Independent Permutations
    76 schema:pagination 113-133
    77 schema:productId Nb48f68274c194aabaee07215ba164c9d
    78 Nd7bbae8afc574eb08e3b7efc809d8d11
    79 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019520288
    80 https://doi.org/10.1007/s00453-008-9267-y
    81 schema:sdDatePublished 2022-01-01T18:19
    82 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    83 schema:sdPublisher N4f9c50101c7e42afa8c99d10458ed620
    84 schema:url https://doi.org/10.1007/s00453-008-9267-y
    85 sgo:license sg:explorer/license/
    86 sgo:sdDataset articles
    87 rdf:type schema:ScholarlyArticle
    88 N37425c5d25264778aa1c5c664ac36c7a schema:volumeNumber 55
    89 rdf:type schema:PublicationVolume
    90 N4f9c50101c7e42afa8c99d10458ed620 schema:name Springer Nature - SN SciGraph project
    91 rdf:type schema:Organization
    92 N556464cdefe14a61b227d5ecd4a69d1b rdf:first sg:person.07776170271.83
    93 rdf:rest Nfdb868b478b742b2a40b27a5cb886641
    94 N56f33d7ac8334e4bb1308818be8903ed schema:issueNumber 1
    95 rdf:type schema:PublicationIssue
    96 Nb48f68274c194aabaee07215ba164c9d schema:name doi
    97 schema:value 10.1007/s00453-008-9267-y
    98 rdf:type schema:PropertyValue
    99 Nc2fdd6d572fc44c5b78036e293a0ec7e rdf:first sg:person.016351357345.24
    100 rdf:rest N556464cdefe14a61b227d5ecd4a69d1b
    101 Nd7bbae8afc574eb08e3b7efc809d8d11 schema:name dimensions_id
    102 schema:value pub.1019520288
    103 rdf:type schema:PropertyValue
    104 Nfdb868b478b742b2a40b27a5cb886641 rdf:first sg:person.012547246003.78
    105 rdf:rest rdf:nil
    106 anzsrc-for:17 schema:inDefinedTermSet anzsrc-for:
    107 schema:name Psychology and Cognitive Sciences
    108 rdf:type schema:DefinedTerm
    109 anzsrc-for:1701 schema:inDefinedTermSet anzsrc-for:
    110 schema:name Psychology
    111 rdf:type schema:DefinedTerm
    112 sg:journal.1047644 schema:issn 0178-4617
    113 1432-0541
    114 schema:name Algorithmica
    115 schema:publisher Springer Nature
    116 rdf:type schema:Periodical
    117 sg:person.012547246003.78 schema:affiliation grid-institutes:grid.13992.30
    118 schema:familyName Reingold
    119 schema:givenName Omer
    120 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012547246003.78
    121 rdf:type schema:Person
    122 sg:person.016351357345.24 schema:affiliation grid-institutes:grid.12136.37
    123 schema:familyName Kaplan
    124 schema:givenName Eyal
    125 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016351357345.24
    126 rdf:type schema:Person
    127 sg:person.07776170271.83 schema:affiliation grid-institutes:grid.13992.30
    128 schema:familyName Naor
    129 schema:givenName Moni
    130 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07776170271.83
    131 rdf:type schema:Person
    132 sg:pub.10.1007/11535218_4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028351668
    133 https://doi.org/10.1007/11535218_4
    134 rdf:type schema:CreativeWork
    135 sg:pub.10.1007/11538462_30 schema:sameAs https://app.dimensions.ai/details/publication/pub.1037921863
    136 https://doi.org/10.1007/11538462_30
    137 rdf:type schema:CreativeWork
    138 sg:pub.10.1007/11538462_37 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047027068
    139 https://doi.org/10.1007/11538462_37
    140 rdf:type schema:CreativeWork
    141 sg:pub.10.1007/3-540-39200-9_34 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018703004
    142 https://doi.org/10.1007/3-540-39200-9_34
    143 rdf:type schema:CreativeWork
    144 sg:pub.10.1007/3-540-45760-7_9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002956912
    145 https://doi.org/10.1007/3-540-45760-7_9
    146 rdf:type schema:CreativeWork
    147 sg:pub.10.1007/3-540-46035-7_9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031230716
    148 https://doi.org/10.1007/3-540-46035-7_9
    149 rdf:type schema:CreativeWork
    150 sg:pub.10.1007/978-1-4419-8594-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008672834
    151 https://doi.org/10.1007/978-1-4419-8594-1
    152 rdf:type schema:CreativeWork
    153 sg:pub.10.1007/978-3-540-24638-1_23 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047813557
    154 https://doi.org/10.1007/978-3-540-24638-1_23
    155 rdf:type schema:CreativeWork
    156 sg:pub.10.1007/978-3-540-24676-3_12 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046250308
    157 https://doi.org/10.1007/978-3-540-24676-3_12
    158 rdf:type schema:CreativeWork
    159 sg:pub.10.1007/978-3-540-27836-8_65 schema:sameAs https://app.dimensions.ai/details/publication/pub.1045310101
    160 https://doi.org/10.1007/978-3-540-27836-8_65
    161 rdf:type schema:CreativeWork
    162 sg:pub.10.1007/978-3-540-28628-8_7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025082760
    163 https://doi.org/10.1007/978-3-540-28628-8_7
    164 rdf:type schema:CreativeWork
    165 sg:pub.10.1007/978-3-540-45146-4_30 schema:sameAs https://app.dimensions.ai/details/publication/pub.1034759171
    166 https://doi.org/10.1007/978-3-540-45146-4_30
    167 rdf:type schema:CreativeWork
    168 sg:pub.10.1007/bf01305237 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019048384
    169 https://doi.org/10.1007/bf01305237
    170 rdf:type schema:CreativeWork
    171 sg:pub.10.1007/pl00003817 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017452659
    172 https://doi.org/10.1007/pl00003817
    173 rdf:type schema:CreativeWork
    174 sg:pub.10.1007/pl00009813 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042491565
    175 https://doi.org/10.1007/pl00009813
    176 rdf:type schema:CreativeWork
    177 sg:pub.10.1023/a:1024632031440 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015226359
    178 https://doi.org/10.1023/a:1024632031440
    179 rdf:type schema:CreativeWork
    180 grid-institutes:grid.12136.37 schema:alternateName Tel-Aviv University, Tel-Aviv, Israel
    181 schema:name Tel-Aviv University, Tel-Aviv, Israel
    182 rdf:type schema:Organization
    183 grid-institutes:grid.13992.30 schema:alternateName Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, 76100, Rehovot, Israel
    184 schema:name Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, 76100, Rehovot, Israel
    185 rdf:type schema:Organization
     




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


    ...