1.

Record Nr.

UNINA9910456558303321

Autore

Cook Stephen <1948->

Titolo

Logical foundations of proof complexity / / Stephen Cook, Phuong Nguyen [[electronic resource]]

Pubbl/distr/stampa

Cambridge : , : Cambridge University Press, , 2010

ISBN

1-107-20671-5

1-282-53611-7

9786612536113

0-511-67967-X

0-511-67842-8

0-511-68165-8

0-511-67716-2

0-511-67627-1

0-511-68363-4

Descrizione fisica

1 online resource (xv, 479 pages) : digital, PDF file(s)

Collana

Perspectives in logic

Disciplina

511.3/6

Soggetti

Computational complexity

Proof theory

Logic, Symbolic and mathematical

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

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

Sommario/riassunto

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.

2.

Record Nr.

UNINA9910790091203321

Autore

Cole G. D. H (George Douglas Howard), <1889-1959.>

Titolo

The world of labour [[electronic resource] ] : a discussion of the present and future of trade unionism / / G.D.H. Cole

Pubbl/distr/stampa

London, : Routledge, 2011

ISBN

1-136-88572-2

1-283-10551-9

9786613105516

0-203-83959-5

Descrizione fisica

1 online resource (229 p.)

Collana

G.D.H. Cole : selected works ; ; v. 3

Disciplina

331.88

331.88/0942

331.880942

Soggetti

Labor unions - Great Britain

Labor unions

Syndicalism

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Reprint. Originally published: London : G. Bell, 1917.

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

BOOK COVER; TITLE01; COPYRIGHT01; TITLE02; PREFACE TO THE 1917



EDITION; PREFACE TO THE 1915 EDITION; PREFACE TO THE FIRST EDITION; CONTENTS; CHAPTER I: MEANS AND ENDS; CHAPTER II: THE LABOUR UNREST; CHAPTER III: LABOUR IN FRANCE; CHAPTER IV: COMMENTS ON THE FRENCH LABOUR MOVEMENT; CHAPTER V: LABOUR IN AMERICA; CHAPTER VI: FURTHER LESSONS FROM ABROAD-THE GENERAL STRIKE; CHAPTER VII: TRADE UNION STRUCTURE-INDUSTRIAL UNIONISM AND AMALGAMATION; CHAPTER VIII: TRADE UNION GOVERNMENT-CENTRALISATION AND LOCAL AUTONOMY; CHAPTER IX: SOCIAL PEACE AND SOCIAL WAR-CONCILIATION AND ARBITRATION

CHAPTER X: LABOUR'S RED HERRINGS-THE FUNCTION OF CO-OPERATIONCHAPTER XI: THE CONTROL OF INDUSTRY-SYNDICALISM AND COLLECTIVISM; CHAPTER XII: THE FUTURE OF TRADE UNIONISM; CHAPTER XIII: ECONOMICS AND POLITICS; CHAPTER XIV: HOPES AND FEARS; BIBLIOGRAPHY; INDEX

Sommario/riassunto

Cole saw the trade unions as being critical to progress, but to realise their role they needed to change and the issue of trade union structure therefore became fundamental. He considered in this volume that trade union structure was a central problem of the labour movement - he described British trade unionism as a movement bereft of ideas and policy. He discusses the evolution in the trade unions to cover not only wages and working conditions but the organisation and control of industry.