Input Products for Weighted Extended Top-Down Tree Transducers View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2010

AUTHORS

Andreas Maletti

ABSTRACT

A weighted tree transformation is a function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\tau \colon T_\Sigma \times T_\Delta \to A$\end{document} where TΣ and TΔ are the sets of trees over the ranked alphabets Σ and Δ, respectively, and A is the domain of a semiring. The input and output product of τ with tree series \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\varphi \colon T_\Sigma \to A$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\psi \colon T_\Delta \to A$\end{document} are the weighted tree transformations \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\varphi \triangleleft \tau$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\tau \triangleright \psi$\end{document}, respectively, which are defined by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(\varphi \triangleleft \tau)(t, u) = \varphi(t) \cdot \tau(t, u)$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(\tau \triangleright \psi)(t, u) = \tau(t, u) \cdot \psi(u)$\end{document} for every t ∈ TΣ and u ∈ TΔ. In this contribution, input and output products of weighted tree transformations computed by weighted extended top-down tree transducers (wxtt) with recognizable tree series are considered. The classical approach is presented and used to solve the simple cases. It is shown that input products can be computed in three successively more difficult scenarios: nondeleting wxtt, wxtt over idempotent semirings, and weighted top-down tree transducers over rings. More... »

PAGES

316-327

Book

TITLE

Developments in Language Theory

ISBN

978-3-642-14454-7
978-3-642-14455-4

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-642-14455-4_29

DOI

http://dx.doi.org/10.1007/978-3-642-14455-4_29

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1048714448


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/2008/11", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Medical and Health Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/1109", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Neurosciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Departament de Filologies Rom\u00e0niques, Universitat Rovira i Virgili, Avinguda de Catalunya 35, 43002, Tarragona, Spain", 
          "id": "http://www.grid.ac/institutes/grid.410367.7", 
          "name": [
            "Departament de Filologies Rom\u00e0niques, Universitat Rovira i Virgili, Avinguda de Catalunya 35, 43002, Tarragona, Spain"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Maletti", 
        "givenName": "Andreas", 
        "id": "sg:person.016645332751.01", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016645332751.01"
        ], 
        "type": "Person"
      }
    ], 
    "datePublished": "2010", 
    "datePublishedReg": "2010-01-01", 
    "description": "A weighted tree transformation is a function\u00a0\\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}$\\tau \\colon T_\\Sigma \\times T_\\Delta \\to A$\\end{document} where T\u03a3\u00a0and\u00a0T\u0394 are the sets of trees over the ranked alphabets \u03a3\u00a0and\u00a0\u0394, respectively, and A\u00a0is the domain of a semiring. The input and output product of\u00a0\u03c4 with tree series \\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}$\\varphi \\colon T_\\Sigma \\to A$\\end{document} and \\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}$\\psi \\colon T_\\Delta \\to A$\\end{document} are the weighted tree transformations \\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}$\\varphi \\triangleleft \\tau$\\end{document}\u00a0and\u00a0\\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}$\\tau \\triangleright \\psi$\\end{document}, respectively, which are defined by \\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}$(\\varphi \\triangleleft \\tau)(t, u) = \\varphi(t) \\cdot \\tau(t, u)$\\end{document} and \\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}$(\\tau \\triangleright \\psi)(t, u) = \\tau(t, u) \\cdot \\psi(u)$\\end{document} for every t\u2009\u2208\u2009T\u03a3 and u\u2009\u2208\u2009T\u0394. In this contribution, input and output products of weighted tree transformations computed by weighted extended top-down tree transducers\u00a0(wxtt) with recognizable tree series are considered. The classical approach is presented and used to solve the simple cases. It is shown that input products can be computed in three successively more difficult scenarios: nondeleting wxtt, wxtt over idempotent semirings, and weighted top-down tree transducers over rings.", 
    "editor": [
      {
        "familyName": "Gao", 
        "givenName": "Yuan", 
        "type": "Person"
      }, 
      {
        "familyName": "Lu", 
        "givenName": "Hanlin", 
        "type": "Person"
      }, 
      {
        "familyName": "Seki", 
        "givenName": "Shinnosuke", 
        "type": "Person"
      }, 
      {
        "familyName": "Yu", 
        "givenName": "Sheng", 
        "type": "Person"
      }
    ], 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-3-642-14455-4_29", 
    "inLanguage": "en", 
    "isAccessibleForFree": false, 
    "isPartOf": {
      "isbn": [
        "978-3-642-14454-7", 
        "978-3-642-14455-4"
      ], 
      "name": "Developments in Language Theory", 
      "type": "Book"
    }, 
    "keywords": [
      "set of trees", 
      "trees", 
      "transducer", 
      "domain", 
      "products", 
      "tree series", 
      "transformation", 
      "function", 
      "input products", 
      "contribution", 
      "set", 
      "classical approach", 
      "input", 
      "series", 
      "tree transformations", 
      "ring", 
      "approach", 
      "scenarios", 
      "tree transducers", 
      "cases", 
      "simple case", 
      "output products", 
      "difficult scenarios", 
      "recognizable tree series", 
      "alphabet \u03a3", 
      "semirings", 
      "idempotent semirings", 
      "weighted tree transformation", 
      "T\u03a3", 
      "T\u0394S", 
      "nondeleting wxtt", 
      "wxtt", 
      "Weighted Extended Top-Down Tree Transducers", 
      "Extended Top-Down Tree Transducers", 
      "Top-Down Tree Transducers"
    ], 
    "name": "Input Products for Weighted Extended Top-Down Tree Transducers", 
    "pagination": "316-327", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1048714448"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-3-642-14455-4_29"
        ]
      }
    ], 
    "publisher": {
      "name": "Springer Nature", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-3-642-14455-4_29", 
      "https://app.dimensions.ai/details/publication/pub.1048714448"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2022-01-01T19:25", 
    "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/chapter/chapter_450.jsonl", 
    "type": "Chapter", 
    "url": "https://doi.org/10.1007/978-3-642-14455-4_29"
  }
]
 

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.10.1007/978-3-642-14455-4_29'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-642-14455-4_29'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-642-14455-4_29'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-642-14455-4_29'


 

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

110 TRIPLES      23 PREDICATES      61 URIs      54 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-3-642-14455-4_29 schema:about anzsrc-for:11
2 anzsrc-for:1109
3 schema:author N4ccc95bf48644e0d88fc8914dcaf9d06
4 schema:datePublished 2010
5 schema:datePublishedReg 2010-01-01
6 schema:description A weighted tree transformation is a function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\tau \colon T_\Sigma \times T_\Delta \to A$\end{document} where TΣ and TΔ are the sets of trees over the ranked alphabets Σ and Δ, respectively, and A is the domain of a semiring. The input and output product of τ with tree series \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\varphi \colon T_\Sigma \to A$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\psi \colon T_\Delta \to A$\end{document} are the weighted tree transformations \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\varphi \triangleleft \tau$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\tau \triangleright \psi$\end{document}, respectively, which are defined by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(\varphi \triangleleft \tau)(t, u) = \varphi(t) \cdot \tau(t, u)$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(\tau \triangleright \psi)(t, u) = \tau(t, u) \cdot \psi(u)$\end{document} for every t ∈ TΣ and u ∈ TΔ. In this contribution, input and output products of weighted tree transformations computed by weighted extended top-down tree transducers (wxtt) with recognizable tree series are considered. The classical approach is presented and used to solve the simple cases. It is shown that input products can be computed in three successively more difficult scenarios: nondeleting wxtt, wxtt over idempotent semirings, and weighted top-down tree transducers over rings.
7 schema:editor N76615541dfef4d118eb64c032234ed9f
8 schema:genre chapter
9 schema:inLanguage en
10 schema:isAccessibleForFree false
11 schema:isPartOf Ndb6fb56e120b4aa88445313cbc1f1583
12 schema:keywords Extended Top-Down Tree Transducers
13 Top-Down Tree Transducers
14 TΔS
15
16 Weighted Extended Top-Down Tree Transducers
17 alphabet Σ
18 approach
19 cases
20 classical approach
21 contribution
22 difficult scenarios
23 domain
24 function
25 idempotent semirings
26 input
27 input products
28 nondeleting wxtt
29 output products
30 products
31 recognizable tree series
32 ring
33 scenarios
34 semirings
35 series
36 set
37 set of trees
38 simple case
39 transducer
40 transformation
41 tree series
42 tree transducers
43 tree transformations
44 trees
45 weighted tree transformation
46 wxtt
47 schema:name Input Products for Weighted Extended Top-Down Tree Transducers
48 schema:pagination 316-327
49 schema:productId N6b80a63849124f0f9b9f631bcc2c0484
50 Nc5d52a5885744e3999020b1dddf5c915
51 schema:publisher N57e4b8c4934740958ec79976c46e5675
52 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048714448
53 https://doi.org/10.1007/978-3-642-14455-4_29
54 schema:sdDatePublished 2022-01-01T19:25
55 schema:sdLicense https://scigraph.springernature.com/explorer/license/
56 schema:sdPublisher N72ae08e6b2044cd4942a007ca9a08e39
57 schema:url https://doi.org/10.1007/978-3-642-14455-4_29
58 sgo:license sg:explorer/license/
59 sgo:sdDataset chapters
60 rdf:type schema:Chapter
61 N03f8f682d4c741e8a0b7c9f6676308b8 schema:familyName Yu
62 schema:givenName Sheng
63 rdf:type schema:Person
64 N095233063259472fa83c19c9a6bbf80e rdf:first N45b80ad75a0f42d0925fdaaf9c5ebe81
65 rdf:rest Nbbfc2997698c47f594ad089b17fa7c50
66 N45b80ad75a0f42d0925fdaaf9c5ebe81 schema:familyName Seki
67 schema:givenName Shinnosuke
68 rdf:type schema:Person
69 N4ccc95bf48644e0d88fc8914dcaf9d06 rdf:first sg:person.016645332751.01
70 rdf:rest rdf:nil
71 N57e4b8c4934740958ec79976c46e5675 schema:name Springer Nature
72 rdf:type schema:Organisation
73 N6b80a63849124f0f9b9f631bcc2c0484 schema:name doi
74 schema:value 10.1007/978-3-642-14455-4_29
75 rdf:type schema:PropertyValue
76 N72ae08e6b2044cd4942a007ca9a08e39 schema:name Springer Nature - SN SciGraph project
77 rdf:type schema:Organization
78 N76615541dfef4d118eb64c032234ed9f rdf:first N8bbb801f50ea40a9a704684b013645d3
79 rdf:rest Nf6bb91d3e5244312b788a20f8b8b9bae
80 N8bbb801f50ea40a9a704684b013645d3 schema:familyName Gao
81 schema:givenName Yuan
82 rdf:type schema:Person
83 Na9589de6de3a4e0886e89b52563e13a7 schema:familyName Lu
84 schema:givenName Hanlin
85 rdf:type schema:Person
86 Nbbfc2997698c47f594ad089b17fa7c50 rdf:first N03f8f682d4c741e8a0b7c9f6676308b8
87 rdf:rest rdf:nil
88 Nc5d52a5885744e3999020b1dddf5c915 schema:name dimensions_id
89 schema:value pub.1048714448
90 rdf:type schema:PropertyValue
91 Ndb6fb56e120b4aa88445313cbc1f1583 schema:isbn 978-3-642-14454-7
92 978-3-642-14455-4
93 schema:name Developments in Language Theory
94 rdf:type schema:Book
95 Nf6bb91d3e5244312b788a20f8b8b9bae rdf:first Na9589de6de3a4e0886e89b52563e13a7
96 rdf:rest N095233063259472fa83c19c9a6bbf80e
97 anzsrc-for:11 schema:inDefinedTermSet anzsrc-for:
98 schema:name Medical and Health Sciences
99 rdf:type schema:DefinedTerm
100 anzsrc-for:1109 schema:inDefinedTermSet anzsrc-for:
101 schema:name Neurosciences
102 rdf:type schema:DefinedTerm
103 sg:person.016645332751.01 schema:affiliation grid-institutes:grid.410367.7
104 schema:familyName Maletti
105 schema:givenName Andreas
106 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016645332751.01
107 rdf:type schema:Person
108 grid-institutes:grid.410367.7 schema:alternateName Departament de Filologies Romàniques, Universitat Rovira i Virgili, Avinguda de Catalunya 35, 43002, Tarragona, Spain
109 schema:name Departament de Filologies Romàniques, Universitat Rovira i Virgili, Avinguda de Catalunya 35, 43002, Tarragona, Spain
110 rdf:type schema:Organization
 




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


...