Metric structures and probabilistic computation
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| Title: | Metric structures and probabilistic computation |
|---|---|
| Authors: | Calvert, Wesley1 wcalvert@sigmaxi.net |
| Source: | Theoretical Computer Science. Jun2011, Vol. 412 Issue 25, p2766-2775. 10p. |
| Subjects: | Model theory, Metric spaces, First-order logic, Hilbert space, Banach spaces, Probability theory, Completeness theorem, Computational complexity |
| Abstract: | Abstract: Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of mathematical objects that can be described in classical first-order logic. The present paper shows that probabilistic computation (sometimes called randomized computation) and continuous logic stand in a similar close relationship. The main result of this paper is an effective completeness theorem, showing that every decidable continuous first-order theory has a probabilistically decidable model. We also show that probabilistically computable structures give rise to a model of in a natural way, and describe a connection with complexity theory. [Copyright &y& Elsevier] |
| Copyright of Theoretical Computer Science is the property of Elsevier B.V. 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 |
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| Header | DbId: egs DbLabel: Engineering Source An: 60161760 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Metric structures and probabilistic computation – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Calvert%2C+Wesley%22">Calvert, Wesley</searchLink><relatesTo>1</relatesTo><i> wcalvert@sigmaxi.net</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Theoretical+Computer+Science%22">Theoretical Computer Science</searchLink>. Jun2011, Vol. 412 Issue 25, p2766-2775. 10p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Model+theory%22">Model theory</searchLink><br /><searchLink fieldCode="DE" term="%22Metric+spaces%22">Metric spaces</searchLink><br /><searchLink fieldCode="DE" term="%22First-order+logic%22">First-order logic</searchLink><br /><searchLink fieldCode="DE" term="%22Hilbert+space%22">Hilbert space</searchLink><br /><searchLink fieldCode="DE" term="%22Banach+spaces%22">Banach spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Probability+theory%22">Probability theory</searchLink><br /><searchLink fieldCode="DE" term="%22Completeness+theorem%22">Completeness theorem</searchLink><br /><searchLink fieldCode="DE" term="%22Computational+complexity%22">Computational complexity</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Abstract: Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of mathematical objects that can be described in classical first-order logic. The present paper shows that probabilistic computation (sometimes called randomized computation) and continuous logic stand in a similar close relationship. The main result of this paper is an effective completeness theorem, showing that every decidable continuous first-order theory has a probabilistically decidable model. We also show that probabilistically computable structures give rise to a model of in a natural way, and describe a connection with complexity theory. [Copyright &y& Elsevier] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Theoretical Computer Science is the property of Elsevier B.V. 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.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.tcs.2011.02.005 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 10 StartPage: 2766 Subjects: – SubjectFull: Model theory Type: general – SubjectFull: Metric spaces Type: general – SubjectFull: First-order logic Type: general – SubjectFull: Hilbert space Type: general – SubjectFull: Banach spaces Type: general – SubjectFull: Probability theory Type: general – SubjectFull: Completeness theorem Type: general – SubjectFull: Computational complexity Type: general Titles: – TitleFull: Metric structures and probabilistic computation Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Calvert, Wesley IsPartOfRelationships: – BibEntity: Dates: – D: 03 M: 06 Text: Jun2011 Type: published Y: 2011 Identifiers: – Type: issn-print Value: 03043975 Numbering: – Type: volume Value: 412 – Type: issue Value: 25 Titles: – TitleFull: Theoretical Computer Science Type: main |
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