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Proof Complexity

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Title: Proof Complexity
Description: Proof complexity is a rich subject drawing on methods from logic, combinatorics, algebra and computer science. This self-contained book presents the basic concepts, classical results, current state of the art and possible future directions in the field. It stresses a view of proof complexity as a whole entity rather than a collection of various topics held together loosely by a few notions, and it favors more generalizable statements. Lower bounds for lengths of proofs, often regarded as the key issue in proof complexity, are of course covered in detail. However, upper bounds are not neglected: this book also explores the relations between bounded arithmetic theories and proof systems and how they can be used to prove upper bounds on lengths of proofs and simulations among proof systems. It goes on to discuss topics that transcend specific proof systems, allowing for deeper understanding of the fundamental problems of the subject.
Authors: Jan Krajíček
Resource Type: eBook.
Subjects: Computational complexity, Proof theory
Categories: MATHEMATICS / Logic
Database: eBook Collection (EBSCOhost)
FullText Links:
  – Type: ebook-pdf
Text:
  Availability: 0
Header DbId: nlebk
DbLabel: eBook Collection (EBSCOhost)
An: 2046158
RelevancyScore: 1090
AccessLevel: 6
PubType: eBook
PubTypeId: ebook
PreciseRelevancyScore: 1090.09973144531
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  Data: Proof Complexity
– Name: Abstract
  Label: Description
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  Data: Proof complexity is a rich subject drawing on methods from logic, combinatorics, algebra and computer science. This self-contained book presents the basic concepts, classical results, current state of the art and possible future directions in the field. It stresses a view of proof complexity as a whole entity rather than a collection of various topics held together loosely by a few notions, and it favors more generalizable statements. Lower bounds for lengths of proofs, often regarded as the key issue in proof complexity, are of course covered in detail. However, upper bounds are not neglected: this book also explores the relations between bounded arithmetic theories and proof systems and how they can be used to prove upper bounds on lengths of proofs and simulations among proof systems. It goes on to discuss topics that transcend specific proof systems, allowing for deeper understanding of the fundamental problems of the subject.
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  Data: <searchLink fieldCode="AR" term="%22Jan+Krajíček%22">Jan Krajíček</searchLink>
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RecordInfo BibRecord:
  BibEntity:
    Classifications:
      – Code: 511.36
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Computational complexity
        Type: general
      – SubjectFull: Proof theory
        Type: general
    Titles:
      – TitleFull: Proof Complexity
        Type: main
  BibRelationships:
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      – PersonEntity:
          Name:
            NameFull: Jan Krajíček
      – PersonEntity:
          Name:
            NameFull: Jan Krajíček
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          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2019
            – D: 03
              M: 04
              Type: profile
              Y: 2019
          Identifiers:
            – Type: isbn-print
              Value: 9781108416849
            – Type: isbn-electronic
              Value: 9781108271585
          Numbering:
            – Type: volume
              Value: 00170
          Titles:
            – TitleFull: Proof Complexity
              Type: main
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