Experiments Concerning the Automated Search for Elegant Proofs PDF Download
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Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 31
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Book Description
The research reported in this technical report was spawned by the request to find an elegant proof (of a theorem from Boolean algebra) to replace the known proof consisting of 816 deduced steps. The request was met by finding a proof consisting of 100 deduced steps. The methodology used to obtain the far shorter proof is presented in detail through a sequence of experiments. Although clearly not an algorithm, the methodology is sufficiently general to enable its use for seeking elegant proofs regardless of the domain of study. The methodology relies heavily on the assistance of McCune's automated reasoning program OTTER. Of the aspects of proof elegance, the main focus here is on proof length, with brief attention paid to the type of term present, the number of variables required, and the complexity of deduced steps. The methodology is iterative, relying heavily on the use of three strategies: the resonance strategy, the hot list strategy, and McCune's ratio strategy. To provide some insight regarding the value of the methodology, the author discusses its successful application to other problems from Boolean algebra and to problems from lattice theory. Research suggestions and challenges are also offered.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 31
Get Book Here
Book Description
The research reported in this technical report was spawned by the request to find an elegant proof (of a theorem from Boolean algebra) to replace the known proof consisting of 816 deduced steps. The request was met by finding a proof consisting of 100 deduced steps. The methodology used to obtain the far shorter proof is presented in detail through a sequence of experiments. Although clearly not an algorithm, the methodology is sufficiently general to enable its use for seeking elegant proofs regardless of the domain of study. The methodology relies heavily on the assistance of McCune's automated reasoning program OTTER. Of the aspects of proof elegance, the main focus here is on proof length, with brief attention paid to the type of term present, the number of variables required, and the complexity of deduced steps. The methodology is iterative, relying heavily on the use of three strategies: the resonance strategy, the hot list strategy, and McCune's ratio strategy. To provide some insight regarding the value of the methodology, the author discusses its successful application to other problems from Boolean algebra and to problems from lattice theory. Research suggestions and challenges are also offered.
Author: Gail W Pieper
Publisher: World Scientific
ISBN: 9814494534
Category : Computers
Languages : en
Pages : 1678
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Book Description
Automated reasoning programs are successfully tackling challenging problems in mathematics and logic, program verification, and circuit design. This two-volume book includes all the published papers of Dr Larry Wos, one of the world's pioneers in automated reasoning. It provides a wealth of information for students, teachers, researchers, and even historians of computer science about this rapidly growing field.The book has the following special features:(1) It presents the strategies introduced by Wos which have made automated reasoning a practical tool for solving challenging puzzles and deep problems in mathematics and logic;(2) It provides a history of the field — from its earliest stages as mechanical theorem proving to its broad base now as automated reasoning;(3) It illustrates some of the remarkable successes automated reasoning programs have had in tackling challenging problems in mathematics, logic, program verification, and circuit design;(4) It includes a CD-ROM, with a searchable index of all the papers, enabling readers to peruse the papers easily for ideas.
Author: Gail W Pieper
Publisher: World Scientific
ISBN: 981449464X
Category : Computers
Languages : en
Pages : 609
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Book Description
This book shows you — through examples and puzzles and intriguing questions — how to make your computer reason logically. To help you, the book includes a CD-ROM with OTTER, the world's most powerful general-purpose reasoning program. The automation of reasoning has advanced markedly in the past few decades, and this book discusses some of the remarkable successes that automated reasoning programs have had in tackling challenging problems in mathematics, logic, program verification, and circuit design. Because the intended audience includes students and teachers, the book provides many exercises (with hints and also answers), as well as tutorial chapters that gently introduce readers to the field of logic and to automated reasoning in general. For more advanced researchers, the book presents challenging questions, many of which are still unsolved.
Author: Francis Su
Publisher: Yale University Press
ISBN: 0300237138
Category : Mathematics
Languages : en
Pages : 287
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Book Description
"The ancient Greeks argued that the best life was filled with beauty, truth, justice, play and love. The mathematician Francis Su knows just where to find them."--Kevin Hartnett, Quanta Magazine" This is perhaps the most important mathematics book of our time. Francis Su shows mathematics is an experience of the mind and, most important, of the heart."--James Tanton, Global Math Project For mathematician Francis Su, a society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas. In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires--such as for play, beauty, freedom, justice, and love--and cultivates virtues essential for human flourishing. These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother's, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher's letters to the author appear throughout the book and show how this intellectual pursuit can--and must--be open to all.
Author: Monty Newborn
Publisher: Springer Science & Business Media
ISBN: 1461300894
Category : Mathematics
Languages : en
Pages : 244
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Book Description
This text and software package introduces readers to automated theorem proving, while providing two approaches implemented as easy-to-use programs. These are semantic-tree theorem proving and resolution-refutation theorem proving. The early chapters introduce first-order predicate calculus, well-formed formulae, and their transformation to clauses. Then the author goes on to show how the two methods work and provides numerous examples for readers to try their hand at theorem-proving experiments. Each chapter comes with exercises designed to familiarise the readers with the ideas and with the software, and answers to many of the problems.
Author: Sungdeok Cha
Publisher: Springer Science & Business Media
ISBN: 354088386X
Category : Computers
Languages : en
Pages : 441
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Book Description
gramatKoreaUniversityandtheDepartmentofComputerScienceatKAISTfor ?nancialsupport. We sincerely hope that the readers ?nd the proceedings of ATVA 2008 informative and rewarding.
Author: Larry Wos
Publisher: Academic Press
ISBN:
Category : Business & Economics
Languages : en
Pages : 456
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Book Description
This book presents some of the insights, judgements, opinions, and experiences gleaned from more than 30 years of research in automated reasoning. The style and organization are those of an experimenter's notebook, featuring both successes and failures resulting from numerous experiments with one of the world's most powerful software packages for automated reasoning, Bill McCune's OTTER.
Author: Richard H. Hammack
Publisher:
ISBN: 9780989472111
Category : Mathematics
Languages : en
Pages : 314
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Book Description
This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.
Author: Frank Pfenning
Publisher: Springer
ISBN: 354073595X
Category : Computers
Languages : en
Pages : 533
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Book Description
A veritable one-stop-shop for anyone looking to get up to speed on what is going down in the field of automated deduction right now. This book contains the refereed proceedings of the 21st International Conference on Automated Deduction, CADE-21, held in Bremen, Germany, in July 2007. The 28 revised full papers and 6 system descriptions presented were selected from 64 submissions. All current aspects of automated deduction are addressed, ranging from theoretical and methodological issues to presentation and evaluation of theorem provers and logical reasoning systems.
Author: Pascal Fontaine
Publisher: Springer Nature
ISBN: 3030294366
Category : Computers
Languages : en
Pages : 603
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Book Description
This book constitutes the proceeding of the 27th International Conference on Automated Deduction, CADE 27, held in Natal, Brazil, in August 2019. The 27 full papers and 7 system descriptions presented were carefully reviewed and selected from 65 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience.
