Logical foundations of proof complexity /:
This book treats bounded arithmetic and propositional proof complexity from the point of view of computational complexity. The first seven chapters include the necessary logical background for the material and are suitable for a graduate course. Associated with each of many complexity classes are bo...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York : Ithaca, NY :
Cambridge University Press ; Association for Symbolic Logic,
©2010.
|
| Schriftenreihe: | Perspectives in logic.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book treats bounded arithmetic and propositional proof complexity from the point of view of computational complexity. The first seven chapters include the necessary logical background for the material and are suitable for a graduate course. Associated with each of many complexity classes are both a two-sorted predicate calculus theory, with induction restricted to concepts in the class, and a propositional proof system. The complexity classes range from AC0 for the weakest theory up to the polynomial hierarchy. Each bounded theorem in a theory translates into a family of (quantified) propositional tautologies with polynomial size proofs in the corresponding proof system. The theory proves the soundness of the associated proof system. The result is a uniform treatment of many systems in the literature, including Buss's theories for the polynomial hierarchy and many disparate systems for complexity classes such as AC0, AC0(m), TC0, NC1, L, NL, NC, and P. |
| Beschreibung: | 1 online resource (xv, 479 pages) : illustrations |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9780511677168 0511677162 9780511681653 0511681658 9780511676277 0511676271 9781107694118 1107694116 1107206715 9781107206717 1282536117 9781282536111 9786612536113 661253611X 0511678428 9780511678424 0511683634 9780511683633 |
Internformat
MARC
| LEADER | 00000cam a2200000 a 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-ocn615625523 | ||
| 003 | OCoLC | ||
| 005 | 20241004212047.0 | ||
| 006 | m o d | ||
| 007 | cr mnu---unuuu | ||
| 008 | 100517s2010 enka ob 001 0 eng d | ||
| 040 | |a N$T |b eng |e pn |c N$T |d OSU |d YDXCP |d OCLCQ |d UKMGB |d OCLCQ |d OCLCF |d AUD |d CUY |d OCLCQ |d PIFAG |d OCLCQ |d WY@ |d LUE |d UAB |d OCLCQ |d OL$ |d OCLCQ |d K6U |d LUN |d QGK |d OCLCO |d OCLCQ |d PSYSI |d OCLCQ |d OCLCO |d OCLCQ |d OCLCL |d SFB | ||
| 016 | 7 | |a 015426824 |2 Uk | |
| 019 | |a 776969815 |a 1170414524 |a 1170659250 |a 1259216045 | ||
| 020 | |a 9780511677168 |q (electronic bk.) | ||
| 020 | |a 0511677162 |q (electronic bk.) | ||
| 020 | |a 9780511681653 |q (ebook) | ||
| 020 | |a 0511681658 |q (ebook) | ||
| 020 | |a 9780511676277 |q (ebook) | ||
| 020 | |a 0511676271 |q (ebook) | ||
| 020 | |z 9780521517294 |q (hardback ; |q alk. paper) | ||
| 020 | |z 052151729X |q (hardback ; |q alk. paper) | ||
| 020 | |a 9781107694118 |q (paperback) | ||
| 020 | |a 1107694116 | ||
| 020 | |a 1107206715 | ||
| 020 | |a 9781107206717 | ||
| 020 | |a 1282536117 | ||
| 020 | |a 9781282536111 | ||
| 020 | |a 9786612536113 | ||
| 020 | |a 661253611X | ||
| 020 | |a 0511678428 | ||
| 020 | |a 9780511678424 | ||
| 020 | |a 0511683634 | ||
| 020 | |a 9780511683633 | ||
| 035 | |a (OCoLC)615625523 |z (OCoLC)776969815 |z (OCoLC)1170414524 |z (OCoLC)1170659250 |z (OCoLC)1259216045 | ||
| 050 | 4 | |a QA267.7 |b .C695 2010eb | |
| 072 | 7 | |a MAT |x 016000 |2 bisacsh | |
| 072 | 7 | |a MAT |x 018000 |2 bisacsh | |
| 082 | 7 | |a 511.3/6 |2 22 | |
| 049 | |a MAIN | ||
| 100 | 1 | |a Cook, Stephen, |d 1948- |1 https://id.oclc.org/worldcat/entity/E39PCjFp7RdW6qKG6fYDdm8PkP |0 http://id.loc.gov/authorities/names/n85180785 | |
| 245 | 1 | 0 | |a Logical foundations of proof complexity / |c Stephen Cook, Phuong Nguyen. |
| 260 | |a Cambridge ; |a New York : |b Cambridge University Press ; |a Ithaca, NY : |b Association for Symbolic Logic, |c ©2010. | ||
| 300 | |a 1 online resource (xv, 479 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Perspectives in logic | |
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a This book treats bounded arithmetic and propositional proof complexity from the point of view of computational complexity. The first seven chapters include the necessary logical background for the material and are suitable for a graduate course. Associated with each of many complexity classes are both a two-sorted predicate calculus theory, with induction restricted to concepts in the class, and a propositional proof system. The complexity classes range from AC0 for the weakest theory up to the polynomial hierarchy. Each bounded theorem in a theory translates into a family of (quantified) propositional tautologies with polynomial size proofs in the corresponding proof system. The theory proves the soundness of the associated proof system. The result is a uniform treatment of many systems in the literature, including Buss's theories for the polynomial hierarchy and many disparate systems for complexity classes such as AC0, AC0(m), TC0, NC1, L, NL, NC, and P. | ||
| 505 | 0 | |a Cover; Half-title; Series-title; Title; Copyright; CONTENTS; PREFACE; Chapter I: INTRODUCTION; Chapter II: THE PREDICATE CALCULUS AND THE SYSTEM LK; Chapter III: PEANO ARITHMETIC AND ITS SUBSYSTEMS; Chapter IV: TWO-SORTED LOGIC AND COMPLEXITY CLASSES; Chapter V: THE THEORY V0 AND AC0; Chapter VI: THE THEORY V1 AND POLYNOMIAL TIME; Chapter VII: PROPOSITIONAL TRANSLATIONS; Chapter VIII: THEORIES FOR POLYNOMIAL TIME AND BEYOND; Chapter IX: THEORIES FOR SMALL CLASSES; Chapter X: PROOF SYSTEMS AND THE REFLECTION PRINCIPLE; Appendix A: COMPUTATION MODELS; BIBLIOGRAPHY; INDEX | |
| 546 | |a English. | ||
| 650 | 0 | |a Computational complexity. |0 http://id.loc.gov/authorities/subjects/sh85029473 | |
| 650 | 0 | |a Proof theory. |0 http://id.loc.gov/authorities/subjects/sh85107437 | |
| 650 | 0 | |a Logic, Symbolic and mathematical. |0 http://id.loc.gov/authorities/subjects/sh85078115 | |
| 650 | 6 | |a Complexité de calcul (Informatique) | |
| 650 | 6 | |a Théorie de la preuve. | |
| 650 | 6 | |a Logique symbolique et mathématique. | |
| 650 | 7 | |a MATHEMATICS |x Infinity. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Logic. |2 bisacsh | |
| 650 | 7 | |a Computational complexity |2 fast | |
| 650 | 7 | |a Logic, Symbolic and mathematical |2 fast | |
| 650 | 7 | |a Proof theory |2 fast | |
| 655 | 0 | |a Electronic books. | |
| 655 | 4 | |a Electronic books. | |
| 700 | 1 | |a Nguyen, Phuong, |d 1977- |1 https://id.oclc.org/worldcat/entity/E39PCjxMHYjCqdTffDJxgvrxym |0 http://id.loc.gov/authorities/names/n2009081816 | |
| 758 | |i has work: |a Logical foundations of proof complexity (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGJyyqcPbF6KXrQxmjTyV3 |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Cook, Stephen, 1948- |t Logical foundations of proof complexity. |d New York : Cambridge University Press ; Ithaca, NY : Association for Symbolic Logic, 2010 |z 9780521517294 |w (DLC) 2009051396 |w (OCoLC)466341175 |
| 830 | 0 | |a Perspectives in logic. |0 http://id.loc.gov/authorities/names/no2009092095 | |
| 856 | 4 | 0 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=313376 |3 Volltext |
| 938 | |a EBSCOhost |b EBSC |n 313376 | ||
| 938 | |a YBP Library Services |b YANK |n 3250779 | ||
| 938 | |a YBP Library Services |b YANK |n 3316902 | ||
| 938 | |a YBP Library Services |b YANK |n 3407670 | ||
| 938 | |a YBP Library Services |b YANK |n 3582404 | ||
| 994 | |a 92 |b GEBAY | ||
| 912 | |a ZDB-4-EBA | ||
| 049 | |a DE-863 | ||
Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn615625523 |
|---|---|
| _version_ | 1816881720370135040 |
| adam_text | |
| any_adam_object | |
| author | Cook, Stephen, 1948- |
| author2 | Nguyen, Phuong, 1977- |
| author2_role | |
| author2_variant | p n pn |
| author_GND | http://id.loc.gov/authorities/names/n85180785 http://id.loc.gov/authorities/names/n2009081816 |
| author_facet | Cook, Stephen, 1948- Nguyen, Phuong, 1977- |
| author_role | |
| author_sort | Cook, Stephen, 1948- |
| author_variant | s c sc |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA267 |
| callnumber-raw | QA267.7 .C695 2010eb |
| callnumber-search | QA267.7 .C695 2010eb |
| callnumber-sort | QA 3267.7 C695 42010EB |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | Cover; Half-title; Series-title; Title; Copyright; CONTENTS; PREFACE; Chapter I: INTRODUCTION; Chapter II: THE PREDICATE CALCULUS AND THE SYSTEM LK; Chapter III: PEANO ARITHMETIC AND ITS SUBSYSTEMS; Chapter IV: TWO-SORTED LOGIC AND COMPLEXITY CLASSES; Chapter V: THE THEORY V0 AND AC0; Chapter VI: THE THEORY V1 AND POLYNOMIAL TIME; Chapter VII: PROPOSITIONAL TRANSLATIONS; Chapter VIII: THEORIES FOR POLYNOMIAL TIME AND BEYOND; Chapter IX: THEORIES FOR SMALL CLASSES; Chapter X: PROOF SYSTEMS AND THE REFLECTION PRINCIPLE; Appendix A: COMPUTATION MODELS; BIBLIOGRAPHY; INDEX |
| ctrlnum | (OCoLC)615625523 |
| dewey-full | 511.3/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/6 |
| dewey-search | 511.3/6 |
| dewey-sort | 3511.3 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>05540cam a2200889 a 4500</leader><controlfield tag="001">ZDB-4-EBA-ocn615625523</controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20241004212047.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr mnu---unuuu</controlfield><controlfield tag="008">100517s2010 enka ob 001 0 eng d</controlfield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">N$T</subfield><subfield code="b">eng</subfield><subfield code="e">pn</subfield><subfield code="c">N$T</subfield><subfield code="d">OSU</subfield><subfield code="d">YDXCP</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">UKMGB</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCF</subfield><subfield code="d">AUD</subfield><subfield code="d">CUY</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">PIFAG</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">WY@</subfield><subfield code="d">LUE</subfield><subfield code="d">UAB</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OL$</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">K6U</subfield><subfield code="d">LUN</subfield><subfield code="d">QGK</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">PSYSI</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCL</subfield><subfield code="d">SFB</subfield></datafield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">015426824</subfield><subfield code="2">Uk</subfield></datafield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">776969815</subfield><subfield code="a">1170414524</subfield><subfield code="a">1170659250</subfield><subfield code="a">1259216045</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780511677168</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0511677162</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780511681653</subfield><subfield code="q">(ebook)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0511681658</subfield><subfield code="q">(ebook)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780511676277</subfield><subfield code="q">(ebook)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0511676271</subfield><subfield code="q">(ebook)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9780521517294</subfield><subfield code="q">(hardback ;</subfield><subfield code="q">alk. paper)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">052151729X</subfield><subfield code="q">(hardback ;</subfield><subfield code="q">alk. paper)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781107694118</subfield><subfield code="q">(paperback)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1107694116</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1107206715</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781107206717</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1282536117</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781282536111</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9786612536113</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">661253611X</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0511678428</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780511678424</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0511683634</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780511683633</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)615625523</subfield><subfield code="z">(OCoLC)776969815</subfield><subfield code="z">(OCoLC)1170414524</subfield><subfield code="z">(OCoLC)1170659250</subfield><subfield code="z">(OCoLC)1259216045</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA267.7</subfield><subfield code="b">.C695 2010eb</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">016000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">018000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">511.3/6</subfield><subfield code="2">22</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Cook, Stephen,</subfield><subfield code="d">1948-</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCjFp7RdW6qKG6fYDdm8PkP</subfield><subfield code="0">http://id.loc.gov/authorities/names/n85180785</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Logical foundations of proof complexity /</subfield><subfield code="c">Stephen Cook, Phuong Nguyen.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">Cambridge ;</subfield><subfield code="a">New York :</subfield><subfield code="b">Cambridge University Press ;</subfield><subfield code="a">Ithaca, NY :</subfield><subfield code="b">Association for Symbolic Logic,</subfield><subfield code="c">©2010.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xv, 479 pages) :</subfield><subfield code="b">illustrations</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Perspectives in logic</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This book treats bounded arithmetic and propositional proof complexity from the point of view of computational complexity. The first seven chapters include the necessary logical background for the material and are suitable for a graduate course. Associated with each of many complexity classes are both a two-sorted predicate calculus theory, with induction restricted to concepts in the class, and a propositional proof system. The complexity classes range from AC0 for the weakest theory up to the polynomial hierarchy. Each bounded theorem in a theory translates into a family of (quantified) propositional tautologies with polynomial size proofs in the corresponding proof system. The theory proves the soundness of the associated proof system. The result is a uniform treatment of many systems in the literature, including Buss's theories for the polynomial hierarchy and many disparate systems for complexity classes such as AC0, AC0(m), TC0, NC1, L, NL, NC, and P.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Cover; Half-title; Series-title; Title; Copyright; CONTENTS; PREFACE; Chapter I: INTRODUCTION; Chapter II: THE PREDICATE CALCULUS AND THE SYSTEM LK; Chapter III: PEANO ARITHMETIC AND ITS SUBSYSTEMS; Chapter IV: TWO-SORTED LOGIC AND COMPLEXITY CLASSES; Chapter V: THE THEORY V0 AND AC0; Chapter VI: THE THEORY V1 AND POLYNOMIAL TIME; Chapter VII: PROPOSITIONAL TRANSLATIONS; Chapter VIII: THEORIES FOR POLYNOMIAL TIME AND BEYOND; Chapter IX: THEORIES FOR SMALL CLASSES; Chapter X: PROOF SYSTEMS AND THE REFLECTION PRINCIPLE; Appendix A: COMPUTATION MODELS; BIBLIOGRAPHY; INDEX</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">English.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Computational complexity.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85029473</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Proof theory.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85107437</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Logic, Symbolic and mathematical.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85078115</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Complexité de calcul (Informatique)</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Théorie de la preuve.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Logique symbolique et mathématique.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Infinity.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Logic.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Computational complexity</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Logic, Symbolic and mathematical</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Proof theory</subfield><subfield code="2">fast</subfield></datafield><datafield tag="655" ind1=" " ind2="0"><subfield code="a">Electronic books.</subfield></datafield><datafield tag="655" ind1=" " ind2="4"><subfield code="a">Electronic books.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Nguyen, Phuong,</subfield><subfield code="d">1977-</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCjxMHYjCqdTffDJxgvrxym</subfield><subfield code="0">http://id.loc.gov/authorities/names/n2009081816</subfield></datafield><datafield tag="758" ind1=" " ind2=" "><subfield code="i">has work:</subfield><subfield code="a">Logical foundations of proof complexity (Text)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCGJyyqcPbF6KXrQxmjTyV3</subfield><subfield code="4">https://id.oclc.org/worldcat/ontology/hasWork</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Cook, Stephen, 1948-</subfield><subfield code="t">Logical foundations of proof complexity.</subfield><subfield code="d">New York : Cambridge University Press ; Ithaca, NY : Association for Symbolic Logic, 2010</subfield><subfield code="z">9780521517294</subfield><subfield code="w">(DLC) 2009051396</subfield><subfield code="w">(OCoLC)466341175</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Perspectives in logic.</subfield><subfield code="0">http://id.loc.gov/authorities/names/no2009092095</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=313376</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">313376</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">3250779</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">3316902</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">3407670</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">3582404</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-863</subfield></datafield></record></collection> |
| genre | Electronic books. |
| genre_facet | Electronic books. |
| id | ZDB-4-EBA-ocn615625523 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:17:12Z |
| institution | BVB |
| isbn | 9780511677168 0511677162 9780511681653 0511681658 9780511676277 0511676271 9781107694118 1107694116 1107206715 9781107206717 1282536117 9781282536111 9786612536113 661253611X 0511678428 9780511678424 0511683634 9780511683633 |
| language | English |
| oclc_num | 615625523 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xv, 479 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Cambridge University Press ; Association for Symbolic Logic, |
| record_format | marc |
| series | Perspectives in logic. |
| series2 | Perspectives in logic |
| spelling | Cook, Stephen, 1948- https://id.oclc.org/worldcat/entity/E39PCjFp7RdW6qKG6fYDdm8PkP http://id.loc.gov/authorities/names/n85180785 Logical foundations of proof complexity / Stephen Cook, Phuong Nguyen. Cambridge ; New York : Cambridge University Press ; Ithaca, NY : Association for Symbolic Logic, ©2010. 1 online resource (xv, 479 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Perspectives in logic Includes bibliographical references and index. Print version record. This book treats bounded arithmetic and propositional proof complexity from the point of view of computational complexity. The first seven chapters include the necessary logical background for the material and are suitable for a graduate course. Associated with each of many complexity classes are both a two-sorted predicate calculus theory, with induction restricted to concepts in the class, and a propositional proof system. The complexity classes range from AC0 for the weakest theory up to the polynomial hierarchy. Each bounded theorem in a theory translates into a family of (quantified) propositional tautologies with polynomial size proofs in the corresponding proof system. The theory proves the soundness of the associated proof system. The result is a uniform treatment of many systems in the literature, including Buss's theories for the polynomial hierarchy and many disparate systems for complexity classes such as AC0, AC0(m), TC0, NC1, L, NL, NC, and P. Cover; Half-title; Series-title; Title; Copyright; CONTENTS; PREFACE; Chapter I: INTRODUCTION; Chapter II: THE PREDICATE CALCULUS AND THE SYSTEM LK; Chapter III: PEANO ARITHMETIC AND ITS SUBSYSTEMS; Chapter IV: TWO-SORTED LOGIC AND COMPLEXITY CLASSES; Chapter V: THE THEORY V0 AND AC0; Chapter VI: THE THEORY V1 AND POLYNOMIAL TIME; Chapter VII: PROPOSITIONAL TRANSLATIONS; Chapter VIII: THEORIES FOR POLYNOMIAL TIME AND BEYOND; Chapter IX: THEORIES FOR SMALL CLASSES; Chapter X: PROOF SYSTEMS AND THE REFLECTION PRINCIPLE; Appendix A: COMPUTATION MODELS; BIBLIOGRAPHY; INDEX English. Computational complexity. http://id.loc.gov/authorities/subjects/sh85029473 Proof theory. http://id.loc.gov/authorities/subjects/sh85107437 Logic, Symbolic and mathematical. http://id.loc.gov/authorities/subjects/sh85078115 Complexité de calcul (Informatique) Théorie de la preuve. Logique symbolique et mathématique. MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Computational complexity fast Logic, Symbolic and mathematical fast Proof theory fast Electronic books. Nguyen, Phuong, 1977- https://id.oclc.org/worldcat/entity/E39PCjxMHYjCqdTffDJxgvrxym http://id.loc.gov/authorities/names/n2009081816 has work: Logical foundations of proof complexity (Text) https://id.oclc.org/worldcat/entity/E39PCGJyyqcPbF6KXrQxmjTyV3 https://id.oclc.org/worldcat/ontology/hasWork Print version: Cook, Stephen, 1948- Logical foundations of proof complexity. New York : Cambridge University Press ; Ithaca, NY : Association for Symbolic Logic, 2010 9780521517294 (DLC) 2009051396 (OCoLC)466341175 Perspectives in logic. http://id.loc.gov/authorities/names/no2009092095 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=313376 Volltext |
| spellingShingle | Cook, Stephen, 1948- Logical foundations of proof complexity / Perspectives in logic. Cover; Half-title; Series-title; Title; Copyright; CONTENTS; PREFACE; Chapter I: INTRODUCTION; Chapter II: THE PREDICATE CALCULUS AND THE SYSTEM LK; Chapter III: PEANO ARITHMETIC AND ITS SUBSYSTEMS; Chapter IV: TWO-SORTED LOGIC AND COMPLEXITY CLASSES; Chapter V: THE THEORY V0 AND AC0; Chapter VI: THE THEORY V1 AND POLYNOMIAL TIME; Chapter VII: PROPOSITIONAL TRANSLATIONS; Chapter VIII: THEORIES FOR POLYNOMIAL TIME AND BEYOND; Chapter IX: THEORIES FOR SMALL CLASSES; Chapter X: PROOF SYSTEMS AND THE REFLECTION PRINCIPLE; Appendix A: COMPUTATION MODELS; BIBLIOGRAPHY; INDEX Computational complexity. http://id.loc.gov/authorities/subjects/sh85029473 Proof theory. http://id.loc.gov/authorities/subjects/sh85107437 Logic, Symbolic and mathematical. http://id.loc.gov/authorities/subjects/sh85078115 Complexité de calcul (Informatique) Théorie de la preuve. Logique symbolique et mathématique. MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Computational complexity fast Logic, Symbolic and mathematical fast Proof theory fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85029473 http://id.loc.gov/authorities/subjects/sh85107437 http://id.loc.gov/authorities/subjects/sh85078115 |
| title | Logical foundations of proof complexity / |
| title_auth | Logical foundations of proof complexity / |
| title_exact_search | Logical foundations of proof complexity / |
| title_full | Logical foundations of proof complexity / Stephen Cook, Phuong Nguyen. |
| title_fullStr | Logical foundations of proof complexity / Stephen Cook, Phuong Nguyen. |
| title_full_unstemmed | Logical foundations of proof complexity / Stephen Cook, Phuong Nguyen. |
| title_short | Logical foundations of proof complexity / |
| title_sort | logical foundations of proof complexity |
| topic | Computational complexity. http://id.loc.gov/authorities/subjects/sh85029473 Proof theory. http://id.loc.gov/authorities/subjects/sh85107437 Logic, Symbolic and mathematical. http://id.loc.gov/authorities/subjects/sh85078115 Complexité de calcul (Informatique) Théorie de la preuve. Logique symbolique et mathématique. MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Computational complexity fast Logic, Symbolic and mathematical fast Proof theory fast |
| topic_facet | Computational complexity. Proof theory. Logic, Symbolic and mathematical. Complexité de calcul (Informatique) Théorie de la preuve. Logique symbolique et mathématique. MATHEMATICS Infinity. MATHEMATICS Logic. Computational complexity Logic, Symbolic and mathematical Proof theory Electronic books. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=313376 |
| work_keys_str_mv | AT cookstephen logicalfoundationsofproofcomplexity AT nguyenphuong logicalfoundationsofproofcomplexity |