Proof complexity /:
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 wh...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, United Kingdom ; New York, NY, USA :
Cambridge University Press,
2019.
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications ;
v. 170. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781108271585 1108271588 9781108242066 1108242065 9781108416849 1108416845 |
Internformat
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| 520 | |a 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. | ||
| 588 | 0 | |a Online resource; title from PDF title page (EBSCO, viewed April 2, 2019). | |
| 505 | 0 | |a Concepts and problems -- Frege systems -- Sequent calculus -- Quantifed propositional calculus -- Resolution -- Algebraic and geometric proof systems -- Further proof systems -- Basic example of the correspondence -- Two worlds of bounded arithmetic -- Up to EF via the <...> translation -- Examples of upper bounds and p-simulations -- Beyond EF via the || ... || translation -- R and R-like proof systems -- LKD+1/2 and combinatorial restrictions -- Fd and logical restrictions -- Algebraic and geometric proof systems -- Feasible interpolation: a framework -- Feasible interpolation: applications -- Hard tautologies -- Model theory and lower bounds -- Optimality -- The nature of proof complexity. | |
| 650 | 0 | |a Proof theory. |0 http://id.loc.gov/authorities/subjects/sh85107437 | |
| 650 | 0 | |a Computational complexity. |0 http://id.loc.gov/authorities/subjects/sh85029473 | |
| 650 | 6 | |a Théorie de la preuve. | |
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| contents | Concepts and problems -- Frege systems -- Sequent calculus -- Quantifed propositional calculus -- Resolution -- Algebraic and geometric proof systems -- Further proof systems -- Basic example of the correspondence -- Two worlds of bounded arithmetic -- Up to EF via the <...> translation -- Examples of upper bounds and p-simulations -- Beyond EF via the || ... || translation -- R and R-like proof systems -- LKD+1/2 and combinatorial restrictions -- Fd and logical restrictions -- Algebraic and geometric proof systems -- Feasible interpolation: a framework -- Feasible interpolation: applications -- Hard tautologies -- Model theory and lower bounds -- Optimality -- The nature of proof complexity. |
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| dewey-raw | 511.3/6 |
| dewey-search | 511.3/6 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-on1090812743 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:29:24Z |
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| isbn | 9781108271585 1108271588 9781108242066 1108242065 9781108416849 1108416845 |
| language | English |
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| series | Encyclopedia of mathematics and its applications ; |
| series2 | Encyclopedia of mathematics and its applications ; |
| spelling | Krajíček, Jan, author. http://id.loc.gov/authorities/names/n92111152 Proof complexity / Jan Krajíček. Cambridge, United Kingdom ; New York, NY, USA : Cambridge University Press, 2019. 1 online resource text txt rdacontent computer c rdamedia online resource cr rdacarrier Encyclopedia of mathematics and its applications ; v. 170 Includes bibliographical references and index. 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. Online resource; title from PDF title page (EBSCO, viewed April 2, 2019). Concepts and problems -- Frege systems -- Sequent calculus -- Quantifed propositional calculus -- Resolution -- Algebraic and geometric proof systems -- Further proof systems -- Basic example of the correspondence -- Two worlds of bounded arithmetic -- Up to EF via the <...> translation -- Examples of upper bounds and p-simulations -- Beyond EF via the || ... || translation -- R and R-like proof systems -- LKD+1/2 and combinatorial restrictions -- Fd and logical restrictions -- Algebraic and geometric proof systems -- Feasible interpolation: a framework -- Feasible interpolation: applications -- Hard tautologies -- Model theory and lower bounds -- Optimality -- The nature of proof complexity. Proof theory. http://id.loc.gov/authorities/subjects/sh85107437 Computational complexity. http://id.loc.gov/authorities/subjects/sh85029473 Théorie de la preuve. Complexité de calcul (Informatique) MATHEMATICS General. bisacsh Complejidad computacional embne Demostración, Teoría de la embucm Computational complexity fast Proof theory fast Electronic book. Encyclopedia of mathematics and its applications ; v. 170. http://id.loc.gov/authorities/names/n42010632 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=2046158 Volltext |
| spellingShingle | Krajíček, Jan Proof complexity / Encyclopedia of mathematics and its applications ; Concepts and problems -- Frege systems -- Sequent calculus -- Quantifed propositional calculus -- Resolution -- Algebraic and geometric proof systems -- Further proof systems -- Basic example of the correspondence -- Two worlds of bounded arithmetic -- Up to EF via the <...> translation -- Examples of upper bounds and p-simulations -- Beyond EF via the || ... || translation -- R and R-like proof systems -- LKD+1/2 and combinatorial restrictions -- Fd and logical restrictions -- Algebraic and geometric proof systems -- Feasible interpolation: a framework -- Feasible interpolation: applications -- Hard tautologies -- Model theory and lower bounds -- Optimality -- The nature of proof complexity. Proof theory. http://id.loc.gov/authorities/subjects/sh85107437 Computational complexity. http://id.loc.gov/authorities/subjects/sh85029473 Théorie de la preuve. Complexité de calcul (Informatique) MATHEMATICS General. bisacsh Complejidad computacional embne Demostración, Teoría de la embucm Computational complexity fast Proof theory fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85107437 http://id.loc.gov/authorities/subjects/sh85029473 |
| title | Proof complexity / |
| title_auth | Proof complexity / |
| title_exact_search | Proof complexity / |
| title_full | Proof complexity / Jan Krajíček. |
| title_fullStr | Proof complexity / Jan Krajíček. |
| title_full_unstemmed | Proof complexity / Jan Krajíček. |
| title_short | Proof complexity / |
| title_sort | proof complexity |
| topic | Proof theory. http://id.loc.gov/authorities/subjects/sh85107437 Computational complexity. http://id.loc.gov/authorities/subjects/sh85029473 Théorie de la preuve. Complexité de calcul (Informatique) MATHEMATICS General. bisacsh Complejidad computacional embne Demostración, Teoría de la embucm Computational complexity fast Proof theory fast |
| topic_facet | Proof theory. Computational complexity. Théorie de la preuve. Complexité de calcul (Informatique) MATHEMATICS General. Complejidad computacional Demostración, Teoría de la Computational complexity Proof theory Electronic book. |
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| work_keys_str_mv | AT krajicekjan proofcomplexity |