Stephen Cook - Böcker

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.

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.

When the coronavirus pandemic took hold early in 2020, charities were among the first to respond to the resulting social and economic distress. But recent scandals and a more critical climate have overshadowed the vital role they play.What Have Charities Ever Done for Us? rebalances the debate, using case studies and interviews to illustrate how charities support people and communities, foster heritage and culture and pioneer responses to crucial social, ethical and environmental questions. It also sets the historical context, examines cases that have attracted criticisms, analyses the political response and considers how the governance, transparency and independence of charities could be improved.Charities at their best are the conscience of society and benefit most people at some point in their lives. This book brings to life the breadth and depth of their work and the contribution they make to social progress.

This book constitutes the referred proceedings of the 5th International Conference on the Unified Modeling Langugage, UML 2002, held in Dresden, Germany in September/October 2002. The 25 revised full research papers and 5 revised experience papers presented were carefully reviewed and selected from 127 abstracts and 99 papers submitted. The papers are organized in topical sections on metamodeling, applying the UML, diggind into the metamodel, experience with MDA, real- time and formal semantics, model engineering, profiles, methodology,and diagram interchange and security.