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Recognizability, hypergraph operations, and logical types

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Title: Recognizability, hypergraph operations, and logical types
Authors: Blumensath, A.1 blumensath@mathematik.tu-darmstadt.de, Courcelle, B.2 courcell@labri.fr
Source: Information & Computation. Jun2006, Vol. 204 Issue 6, p853-919. 67p.
Subjects: Hypergraphs, Algebra, Mathematical analysis, Graph theory
Abstract: Abstract: We study several algebras of graphs and hypergraphs and the corresponding notions of equational sets and recognizable sets. We generalize and unify several existing results which compare the associated equational and recognizable sets. The basic algebra on relational structures is based on disjoint union and quantifier-free definable operations. We expand it to an equivalent one by adding operations definable with “few quantifiers”, i.e., operations that take into account local information about elements or tuples. We also consider monadic second-order transductions and we prove that the inverse image of a recognizable set under such a transduction is recognizable. [Copyright &y& Elsevier]
Copyright of Information & Computation is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
FullText Text:
  Availability: 0
Header DbId: egs
DbLabel: Engineering Source
An: 20900944
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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IllustrationInfo
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  Data: Recognizability, hypergraph operations, and logical types
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  Data: <searchLink fieldCode="AR" term="%22Blumensath%2C+A%2E%22">Blumensath, A.</searchLink><relatesTo>1</relatesTo><i> blumensath@mathematik.tu-darmstadt.de</i><br /><searchLink fieldCode="AR" term="%22Courcelle%2C+B%2E%22">Courcelle, B.</searchLink><relatesTo>2</relatesTo><i> courcell@labri.fr</i>
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  Data: <searchLink fieldCode="JN" term="%22Information+%26+Computation%22">Information & Computation</searchLink>. Jun2006, Vol. 204 Issue 6, p853-919. 67p.
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  Data: <searchLink fieldCode="DE" term="%22Hypergraphs%22">Hypergraphs</searchLink><br /><searchLink fieldCode="DE" term="%22Algebra%22">Algebra</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+analysis%22">Mathematical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink>
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  Data: Abstract: We study several algebras of graphs and hypergraphs and the corresponding notions of equational sets and recognizable sets. We generalize and unify several existing results which compare the associated equational and recognizable sets. The basic algebra on relational structures is based on disjoint union and quantifier-free definable operations. We expand it to an equivalent one by adding operations definable with “few quantifiers”, i.e., operations that take into account local information about elements or tuples. We also consider monadic second-order transductions and we prove that the inverse image of a recognizable set under such a transduction is recognizable. [Copyright &y& Elsevier]
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  Data: <i>Copyright of Information & Computation is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=20900944
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        Value: 10.1016/j.ic.2005.11.006
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        Text: English
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      – SubjectFull: Graph theory
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      – TitleFull: Recognizability, hypergraph operations, and logical types
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              Text: Jun2006
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