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| boolean pythagorean triples problem: Handbook of Parallel Constraint Reasoning Youssef Hamadi, Lakhdar Sais, 2018-04-05 This is the first book presenting a broad overview of parallelism in constraint-based reasoning formalisms. In recent years, an increasing number of contributions have been made on scaling constraint reasoning thanks to parallel architectures. The goal in this book is to overview these achievements in a concise way, assuming the reader is familiar with the classical, sequential background. It presents work demonstrating the use of multiple resources from single machine multi-core and GPU-based computations to very large scale distributed execution platforms up to 80,000 processing units. The contributions in the book cover the most important and recent contributions in parallel propositional satisfiability (SAT), maximum satisfiability (MaxSAT), quantified Boolean formulas (QBF), satisfiability modulo theory (SMT), theorem proving (TP), answer set programming (ASP), mixed integer linear programming (MILP), constraint programming (CP), stochastic local search (SLS), optimal path finding with A*, model checking for linear-time temporal logic (MC/LTL), binary decision diagrams (BDD), and model-based diagnosis (MBD). The book is suitable for researchers, graduate students, advanced undergraduates, and practitioners who wish to learn about the state of the art in parallel constraint reasoning. |
| boolean pythagorean triples problem: Theory and Applications of Satisfiability Testing – SAT 2016 Nadia Creignou, Daniel Le Berre, 2016-06-10 This book constitutes the refereed proceedings of the 19th International Conference on Theory and Applications of Satisfiability Testing, SAT 2016, held in Bordeaux, France, in July 2016. The 31 regular papers, 5 tool papers presented together with 3 invited talks were carefully reviewed and selected from 70 submissions. The papers address different aspects of SAT, including complexity, satisfiability solving, satisfiability applications, satisfiability modulop theory, beyond SAT, quantified Boolean formula, and dependency QBF. |
| boolean pythagorean triples problem: Parallel Problem Solving from Nature – PPSN XVI Thomas Bäck, Mike Preuss, André Deutz, Hao Wang, Carola Doerr, Michael Emmerich, Heike Trautmann, 2020-09-02 This two-volume set LNCS 12269 and LNCS 12270 constitutes the refereed proceedings of the 16th International Conference on Parallel Problem Solving from Nature, PPSN 2020, held in Leiden, The Netherlands, in September 2020. The 99 revised full papers were carefully reviewed and selected from 268 submissions. The topics cover classical subjects such as automated algorithm selection and configuration; Bayesian- and surrogate-assisted optimization; benchmarking and performance measures; combinatorial optimization; connection between nature-inspired optimization and artificial intelligence; genetic and evolutionary algorithms; genetic programming; landscape analysis; multiobjective optimization; real-world applications; reinforcement learning; and theoretical aspects of nature-inspired optimization. |
| boolean pythagorean triples problem: Logic Functions and Equations Bernd Steinbach, Christian Posthoff, 2022-06-06 The greatly expanded and updated 3rd edition of this textbook offers the reader a comprehensive introduction to the concepts of logic functions and equations and their applications across computer science and engineering. The authors’ approach emphasizes a thorough understanding of the fundamental principles as well as numerical and computer-based solution methods. The book provides insight into applications across propositional logic, binary arithmetic, coding, cryptography, complexity, logic design, and artificial intelligence. Updated throughout, some major additions for the 3rd edition include: a new chapter about the concepts contributing to the power of XBOOLE; a new chapter that introduces into the application of the XBOOLE-Monitor XBM 2; many tasks that support the readers in amplifying the learned content at the end of the chapters; solutions of a large subset of these tasks to confirm learning success; challenging tasks that need the power of the XBOOLE software for their solution. The XBOOLE-monitor XBM 2 software is used to solve the exercises; in this way the time-consuming and error-prone manipulation on the bit level is moved to an ordinary PC, more realistic tasks can be solved, and the challenges of thinking about algorithms leads to a higher level of education. |
| boolean pythagorean triples problem: Thinking Programs Wolfgang Schreiner, 2021-10-22 This book describes some basic principles that allow developers of computer programs (computer scientists, software engineers, programmers) to clearly think about the artifacts they deal with in their daily work: data types, programming languages, programs written in these languages that compute from given inputs wanted outputs, and programs that describe continuously executing systems. The core message is that clear thinking about programs can be expressed in a single universal language, the formal language of logic. Apart from its universal elegance and expressiveness, this “logical” approach to the formal modeling of and reasoning about computer programs has another advantage: due to advances in computational logic (automated theorem proving, satisfiability solving, model checking), nowadays much of this process can be supported by software. This book therefore accompanies its theoretical elaborations by practical demonstrations of various systems and tools that are based on respectively make use of the presented logical underpinnings. |
| boolean pythagorean triples problem: Ramsey Theory Xiaodong Xu, Meilian Liang, Haipeng Luo, 2018-08-06 Key problems and conjectures have played an important role in promoting the development of Ramsey theory, a field where great progress has been made during the past two decades, with some old problems solved and many new problems proposed. The present book will be helpful to readers who wish to learn about interesting problems in Ramsey theory, to see how they are interconnected, and then to study them in depth. This book is the first problem book of such scope in Ramsey theory. Many unsolved problems, conjectures and related partial results in Ramsey theory are presented, in areas such as extremal graph theory, additive number theory, discrete geometry, functional analysis, algorithm design, and in other areas. Most presented problems are easy to understand, but they may be difficult to solve. They can be appreciated on many levels and by a wide readership, ranging from undergraduate students majoring in mathematics to research mathematicians. This collection is an essential reference for mathematicians working in combinatorics and number theory, as well as for computer scientists studying algorithms. Contents Some definitions and notations Ramsey theory Bi-color diagonal classical Ramsey numbers Paley graphs and lower bounds for R(k, k) Bi-color off-diagonal classical Ramsey numbers Multicolor classical Ramsey numbers Generalized Ramsey numbers Folkman numbers The Erdős–Hajnal conjecture Other Ramsey-type problems in graph theory On van der Waerden numbers and Szemeredi’s theorem More problems of Ramsey type in additive number theory Sidon–Ramsey numbers Games in Ramsey theory Local Ramsey theory Set-coloring Ramsey theory Other problems and conjectures |
| boolean pythagorean triples problem: Revolutionary Mathematics Justin Joque, 2022-01-18 Traces the revolution in statistics that gave rise to artificial intelligence and predictive algorithms refiguring contemporary capitalism. Our finances, politics, media, opportunities, information, shopping and knowledge production are mediated through algorithms and their statistical approaches to knowledge; increasingly, these methods form the organizational backbone of contemporary capitalism. Revolutionary Mathematics traces the revolution in statistics and probability that has quietly underwritten the explosion of machine learning, big data and predictive algorithms that now decide many aspects of our lives. Exploring shifts in the philosophical understanding of probability in the late twentieth century, Joque shows how this was not merely a technical change but a wholesale philosophical transformation in the production of knowledge and the extraction of value. This book provides a new and unique perspective on the dangers of allowing artificial intelligence and big data to manage society. It is essential reading for those who want to understand the underlying ideological and philosophical changes that have fueled the rise of algorithms and convinced so many to blindly trust their outputs, reshaping our current political and economic situation. |
| boolean pythagorean triples problem: Discrete Encounters Craig Bauer, 2020-05-14 Eschewing the often standard dry and static writing style of traditional textbooks, Discrete Encounters provides a refreshing approach to discrete mathematics. The author blends traditional course topics and applications with historical context, pop culture references, and open problems. This book focuses on the historical development of the subject and provides fascinating details of the people behind the mathematics, along with their motivations, deepening readers’ appreciation of mathematics. This unique book covers many of the same topics found in traditional textbooks, but does so in an alternative, entertaining style that better captures readers’ attention. In addition to standard discrete mathematics material, the author shows the interplay between the discrete and the continuous and includes high-interest topics such as fractals, chaos theory, cellular automata, money-saving financial mathematics, and much more. Not only will readers gain a greater understanding of mathematics and its culture, they will also be encouraged to further explore the subject. Long lists of references at the end of each chapter make this easy. Highlights: Features fascinating historical context to motivate readers Text includes numerous pop culture references throughout to provide a more engaging reading experience Its unique topic structure presents a fresh approach The text’s narrative style is that of a popular book, not a dry textbook Includes the work of many living mathematicians Its multidisciplinary approach makes it ideal for liberal arts mathematics classes, leisure reading, or as a reference for professors looking to supplement traditional courses Contains many open problems Profusely illustrated |
| boolean pythagorean triples problem: Leveraging Applications of Formal Methods, Verification and Validation. Software Engineering Methodologies Tiziana Margaria, |
| boolean pythagorean triples problem: Automated Deduction – CADE 26 Leonardo de Moura, 2017-07-09 This book constitutes the proceeding of the 26th International Conference on Automated Deduction, CADE-26, held in Gothenburg, Sweden, in August 2017. The 26 full papers and 5 system descriptions presented were carefully reviewed and selected from 69 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations and practical experience. The chapter 'Certifying Confluence of Quasi-Decreasing Strongly Deterministic Conditional Term Rewrite Systems' is published open access under a CC BY 4.0 license. |
| boolean pythagorean triples problem: Automated Reasoning Nicolas Peltier, Viorica Sofronie-Stokkermans, 2020-06-30 This two-volume set LNAI 12166 and 12167 constitutes the refereed proceedings of the 10th International Joint Conference on Automated Reasoning, IJCAR 2020, held in Paris, France, in July 2020.* In 2020, IJCAR was a merger of the following leading events, namely CADE (International Conference on Automated Deduction), FroCoS (International Symposium on Frontiers of Combining Systems), ITP (International Conference on Interactive Theorem Proving), and TABLEAUX (International Conference on Analytic Tableaux and Related Methods). The 46 full research papers, 5 short papers, and 11 system descriptions presented together with two invited talks were carefully reviewed and selected from 150 submissions. The papers focus on the following topics: Part I: SAT; SMT and QBF; decision procedures and combination of theories; superposition; proof procedures; non classical logics Part II: interactive theorem proving/ HOL; formalizations; verification; reasoning systems and tools *The conference was held virtually due to the COVID-19 pandemic. Chapter ‘Constructive Hybrid Games’ is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com. |
| boolean pythagorean triples problem: NASA Formal Methods Julia M. Badger, Kristin Yvonne Rozier, 2019-05-28 This book constitutes the proceedings of the 11th International Symposium on NASA Formal Methods, NFM 2019, held in Houston, TX, USA, in May 2019. The 20 full and 8 short papers presented in this volume were carefully reviewed and selected from 102 submissions. The papers focus on formal verification, including theorem proving, model checking, and static analysis; advances in automated theorem proving including SAT and SMT solving; use of formal methods in software and system testing; run-time verification; techniques and algorithms for scaling formal methods, such as abstraction and symbolic methods, compositional techniques, as well as parallel and/or distributed techniques; code generation from formally verified models; safety cases and system safety; formal approaches to fault tolerance; theoretical advances and empirical evaluations of formal methods techniques for safety-critical systems, including hybrid and embedded systems; formal methods in systems engineering and model-based development; correct-by-design controller synthesis; formal assurance methods to handle adaptive systems. |
| boolean pythagorean triples problem: Intelligent Computer Mathematics Kevin Buzzard, Temur Kutsia, 2022-09-16 This book constitutes the refereed proceedings of the 15th International Conference on Intelligent Computer Mathematics, CICM 2022, held in Tbilisi, Georgia, in September 2022. The 17 full papers, 1 project/ survey paper, 4 short papers, and 2 abstracts of invited papers presented were carefully reviewed and selected from a total of 37 submissions. The papers focus on theoretical and practical solutions for these challenges including computation, deduction, narration, and data management. |
| boolean pythagorean triples problem: Effective Theories in Programming Practice Jayadev Misra, 2022-12-27 Set theory, logic, discrete mathematics, and fundamental algorithms (along with their correctness and complexity analysis) will always remain useful for computing professionals and need to be understood by students who want to succeed. This textbook explains a number of those fundamental algorithms to programming students in a concise, yet precise, manner. The book includes the background material needed to understand the explanations and to develop such explanations for other algorithms. The author demonstrates that clarity and simplicity are achieved not by avoiding formalism, but by using it properly. The book is self-contained, assuming only a background in high school mathematics and elementary program writing skills. It does not assume familiarity with any specific programming language. Starting with basic concepts of sets, functions, relations, logic, and proof techniques including induction, the necessary mathematical framework for reasoning about the correctness, termination and efficiency of programs is introduced with examples at each stage. The book contains the systematic development, from appropriate theories, of a variety of fundamental algorithms related to search, sorting, matching, graph-related problems, recursive programming methodology and dynamic programming techniques, culminating in parallel recursive structures. |
| boolean pythagorean triples problem: Implementation and Application of Automata Sebastian Maneth, 2021-06-22 This book constitutes the proceedings of the 25th International Conference on Implementation and Application of Automata, CIAA 2021, held in July 2021. Due to Covid-19 pandemic the conference was held virtually. The 13 regular papers presented in this book were carefully reviewed and selected from 20 submissions. The topics of the papers cover various fields in the application, implementation, and theory of automata and related structures. |
| boolean pythagorean triples problem: AI Roman V. Yampolskiy, 2024-02-23 Delving into the deeply enigmatic nature of Artificial Intelligence (AI), AI: Unexplainable, Unpredictable, Uncontrollable explores the various reasons why the field is so challenging. Written by one of the founders of the field of AI safety, this book addresses some of the most fascinating questions facing humanity, including the nature of intelligence, consciousness, values and knowledge. Moving from a broad introduction to the core problems, such as the unpredictability of AI outcomes or the difficulty in explaining AI decisions, this book arrives at more complex questions of ownership and control, conducting an in-depth analysis of potential hazards and unintentional consequences. The book then concludes with philosophical and existential considerations, probing into questions of AI personhood, consciousness, and the distinction between human intelligence and artificial general intelligence (AGI). Bridging the gap between technical intricacies and philosophical musings, AI: Unexplainable, Unpredictable, Uncontrollable appeals to both AI experts and enthusiasts looking for a comprehensive understanding of the field, whilst also being written for a general audience with minimal technical jargon. |
| boolean pythagorean triples problem: Fundamentals of Ramsey Theory Aaron Robertson, 2021-06-17 Ramsey theory is a fascinating topic. The author shares his view of the topic in this contemporary overview of Ramsey theory. He presents from several points of view, adding intuition and detailed proofs, in an accessible manner unique among most books on the topic. This book covers all of the main results in Ramsey theory along with results that have not appeared in a book before. The presentation is comprehensive and reader friendly. The book covers integer, graph, and Euclidean Ramsey theory with many proofs being combinatorial in nature. The author motivates topics and discussion, rather than just a list of theorems and proofs. In order to engage the reader, each chapter has a section of exercises. This up-to-date book introduces the field of Ramsey theory from several different viewpoints so that the reader can decide which flavor of Ramsey theory best suits them. Additionally, the book offers: A chapter providing different approaches to Ramsey theory, e.g., using topological dynamics, ergodic systems, and algebra in the Stone-Čech compactification of the integers. A chapter on the probabilistic method since it is quite central to Ramsey-type numbers. A unique chapter presenting some applications of Ramsey theory. Exercises in every chapter The intended audience consists of students and mathematicians desiring to learn about Ramsey theory. An undergraduate degree in mathematics (or its equivalent for advanced undergraduates) and a combinatorics course is assumed. TABLE OF CONENTS Preface List of Figures List of Tables Symbols 1. Introduction 2. Integer Ramsey Theory 3. Graph Ramsey Theory 4. Euclidean Ramsey Theory 5. Other Approaches to Ramsey Theory 6. The Probabilistic Method 7. Applications Bibliography Index Biography Aaron Robertson received his Ph.D. in mathematics from Temple University under the guidance of his advisor Doron Zeilberger. Upon finishing his Ph.D. he started at Colgate University in upstate New York where he is currently Professor of Mathematics. He also serves as Associate Managing editor of the journal Integers. After a brief detour into the world of permutation patterns, he has focused most of his research on Ramsey theory. |
| boolean pythagorean triples problem: Theoretical Aspects of Computing – ICTAC 2023 Erika Ábrahám, Clemens Dubslaff, Silvia Lizeth Tapia Tarifa, 2023-12-24 This book constitutes the proceedings of the 20th International Colloquium on Theoretical Aspects of Computing, ICTAC 2023, which took place in Lima, Peru, during December 4–8, 2023. The 20 full papers presented in this volume together with 3 invited papers and 1 tool paper were carefully reviewed and selected from 40 submissions. They were organised in the topical sections as follows: Bring Together Practitioners; Researchers from Academia; Industry; Government to Present Research Results and Exchange Experience and Ideas. |
| boolean pythagorean triples problem: Automated Reasoning Jasmin Blanchette, Laura Kovács, Dirk Pattinson, 2022 This is an open access book. It is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com. |
| boolean pythagorean triples problem: Trends in Computational Social Choice Ulle Endriss, 2017 Computational social choice is concerned with the design and analysis of methods for collective decision making. It is a research area that is located at the interface of computer science and economics. The central question studied in computational social choice is that of how best to aggregate the individual points of view of several agents, so as to arrive at a reasonable compromise. Examples include tallying the votes cast in an election, aggregating the professional opinions of several experts, and finding a fair manner of dividing a set of resources amongst the members of a group -- Back cover. |
| boolean pythagorean triples problem: Parallel Computational Technologies Leonid Sokolinsky, Mikhail Zymbler, 2023-07-24 This book constitutes the refereed post proceedings of the 17th International Conference on Parallel Computational Technologies, PCT 2023, held in Saint Petersburg, Russia, during March 28–30, 2023. The 25 full papers included in this book were carefully reviewed and selected from 71 submissions. They were organized in topical sections as follows: High Performance Architectures, Tools and Technologies, Parallel Numerical Algorithms, and Supercomputer Simulation. |
| boolean pythagorean triples problem: Tools and Algorithms for the Construction and Analysis of Systems Axel Legay, Tiziana Margaria, 2017-03-30 The two-book set LNCS 10205 + 10206 constitutes the proceedings of the 23rd International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2017, which took place in Uppsala, Sweden in April 2017, held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2017. The 48 full papers, 4 tool demonstration papers, and 12 software competition papers presented in these volumes were carefully reviewed and selected from 181 submissions to TACAS and 32 submissions to the software competition. They were organized in topical sections named: verification techniques; learning; synthesis; automata; concurrency and bisimulation; hybrid systems; security; run-time verification and logic; quantitative systems; SAT and SMT; and SV COMP. |
| boolean pythagorean triples problem: Proof Technology in Mathematics Research and Teaching Gila Hanna, David A. Reid, Michael de Villiers, 2019-10-02 This book presents chapters exploring the most recent developments in the role of technology in proving. The full range of topics related to this theme are explored, including computer proving, digital collaboration among mathematicians, mathematics teaching in schools and universities, and the use of the internet as a site of proof learning. Proving is sometimes thought to be the aspect of mathematical activity most resistant to the influence of technological change. While computational methods are well known to have a huge importance in applied mathematics, there is a perception that mathematicians seeking to derive new mathematical results are unaffected by the digital era. The reality is quite different. Digital technologies have transformed how mathematicians work together, how proof is taught in schools and universities, and even the nature of proof itself. Checking billions of cases in extremely large but finite sets, impossible a few decades ago, has now become a standard method of proof. Distributed proving, by teams of mathematicians working independently on sections of a problem, has become very much easier as digital communication facilitates the sharing and comparison of results. Proof assistants and dynamic proof environments have influenced the verification or refutation of conjectures, and ultimately how and why proof is taught in schools. And techniques from computer science for checking the validity of programs are being used to verify mathematical proofs. Chapters in this book include not only research reports and case studies, but also theoretical essays, reviews of the state of the art in selected areas, and historical studies. The authors are experts in the field. |
| boolean pythagorean triples problem: Automated Deduction - CADE 28 André Platzer, 2021 This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions. |
| boolean pythagorean triples problem: Tools and Algorithms for the Construction and Analysis of Systems Jan Friso Groote, Kim Guldstrand Larsen, 2021-03-22 This open access two-volume set constitutes the proceedings of the 27th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2021, which was held during March 27 – April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The total of 41 full papers presented in the proceedings was carefully reviewed and selected from 141 submissions. The volume also contains 7 tool papers; 6 Tool Demo papers, 9 SV-Comp Competition Papers. The papers are organized in topical sections as follows: Part I: Game Theory; SMT Verification; Probabilities; Timed Systems; Neural Networks; Analysis of Network Communication. Part II: Verification Techniques (not SMT); Case Studies; Proof Generation/Validation; Tool Papers; Tool Demo Papers; SV-Comp Tool Competition Papers. |
| boolean pythagorean triples problem: Theory and Applications of Satisfiability Testing – SAT 2020 Luca Pulina, Martina Seidl, 2020-07-01 This book constitutes the proceedings of the 23rd International Conference on Theory and Applications of Satisfiability Testing, SAT 2020, which was planned to take place in Alghero, Italy, during July 5-9, 2020. Due to the coronavirus COVID-19 pandemic, the conference was held virtually. The 25 full, 9 short, and 2 tool papers presented in this volume were carefully reviewed and selected from 69 submissions. They deal with SAT interpreted in a broad sense, including theoretical advances (such as exact algorithms, proof complexity, and other complexity issues), practical search algorithms, knowledge compilation, implementation-level details of SAT solvers and SAT-based systems, problem encodings and reformulations, applications (including both novel application domains and improvements to existing approaches), as well as case studies and reports on findings based on rigorous experimentation. |
| boolean pythagorean triples problem: Computer Algebra in Scientific Computing Vladimir P. Gerdt, Wolfram Koepf, Werner M. Seiler, Evgenii V. Vorozhtsov, 2016-09-08 This book constitutes the proceedings of the 18th International Workshop on Computer Algebra in Scientific Computing, CASC 2016, held in Bucharest, Romania, in September 2016. The 32 papers presented in this volume were carefully reviewed and selected from 39 submissions. They deal with cutting-edge research in all major disciplines of Computer Algebra. |
| boolean pythagorean triples problem: Tests and Proofs Virgile Prevosto, Cristina Seceleanu, 2023-07-19 This book constitutes the proceedings of the 17th International Conference, TAP 2023, as part of STAF 2023, a federation of conferences on Software Technologies, Applications and Foundations, which includes two more conferences besides TAP: ICGT (International Conference on Graph Transformations), and ECMFA (European Conference on Modelling Foundations and Applications) in Leicester, UK, in July 2023. The 8 full papers together with 2 short papers included in this volume were carefully reviewed and selected from 14 submissions. They were organized in topical sections on Low-level Code Verification, Formal Models, Model-based test generation, and Abstraction and Refinement. |
| boolean pythagorean triples problem: PROCEEDINGS OF THE 21ST CONFERENCE ON FORMAL METHODS IN COMPUTER-AIDED DESIGN – FMCAD 2021 Michael W. Whalen, Ruzica Piskac, 2021-10-14 Our life is dominated by hardware: a USB stick, the processor in our laptops or the SIM card in our smart phone. But who or what makes sure that these systems work stably, safely and securely from the word go? The computer - with a little help from humans. The overall name for this is CAD (computer-aided design), and it’s become hard to imagine our modern industrial world without it. So how can we be sure that the hardware and computer systems we use are reliable? By using formal methods: these are techniques and tools to calculate whether a system description is in itself consistent or whether requirements have been developed and implemented correctly. Or to put it another way: they can be used to check the safety and security of hardware and software. Just how this works in real life was also of interest at the annual conference on Formal Methods in Computer-Aided Design (FMCAD). Under the direction of Ruzica Piskac and Michael Whalen, the 21st Conference in October 2021 addressed the results of the latest research in the field of formal methods. A volume of conference proceedings with over 30 articles covering a wide range of formal methods has now been published for this online conference: starting from the verification of hardware, parallel and distributed systems as well as neuronal networks, right through to machine learning and decision-making procedures. This volume provides a fascinating insight into revolutionary methods, technologies, theoretical results and tools for formal logic in computer systems and system developments. |
| boolean pythagorean triples problem: Combinatorial Algorithms Leszek Gąsieniec, Ralf Klasing, Tomasz Radzik, 2020-05-28 This book constitutes the proceedings of the 31st International Workshop on Combinatorial Algorithms which was planned to take place in Bordeaux, France, during June 8–10, 2020. Due to the COVID-19 pandemic the conference changed to a virtual format. The 30 full papers included in this book were carefully reviewed and selected from 62 submissions. They focus on algorithms design for the myriad of combinatorial problems that underlie computer applications in science, engineering and business. |
| boolean pythagorean triples problem: PROCEEDINGS OF THE 23RD CONFERENCE ON FORMAL METHODS IN COMPUTER-AIDED DESIGN – FMCAD 2023 Alexander Nadel , Kristin Yvonne Rozier, 2023-10-13 The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system testing. |
| boolean pythagorean triples problem: Theory and Applications of Satisfiability Testing – SAT 2021 Chu-Min Li, Felip Manyà, 2021-07-01 This book constitutes the proceedings of the 24th International Conference on Theory and Applications of Satisfiability Testing, SAT 2021, which took place in Barcelona, Spain, in July 2021. The 37 full papers presented in this volume were carefully reviewed and selected from 73 submissions. They deal with theory and applications of the propositional satisfiability problem, broadly construed. Aside from plain propositional satisfiability, the scope of the meeting includes Boolean optimization, including MaxSAT and pseudo-Boolean (PB) constraints, quantified Boolean formulas (QBF), satisfiability modulo theories (SMT), and constraint programming (CP) for problems with clear connections to Boolean reasoning. |
| boolean pythagorean triples problem: Theory and Applications of Satisfiability Testing – SAT 2019 Mikoláš Janota, Inês Lynce, 2019-06-28 This book constitutes the refereed proceedings of the 22nd International Conference on Theory and Applications of Satisfiability Testing, SAT 2019, held in Lisbon, Portugal, UK, in July 2019. The 19 revised full papers presented together with 7 short papers were carefully reviewed and selected from 64 submissions. The papers address different aspects of SAT interpreted in a broad sense, including (but not restricted to) theoretical advances (such as exact algorithms, proof complexity, and other complexity issues), practical search algorithms, knowledge compilation, implementation-level details of SAT solvers and SAT-based systems, problem encodings and reformulations, applications (including both novel application domains and improvements to existing approaches), as well as case studies and reports on findings based on rigorous experimentation. |
| boolean pythagorean triples problem: Intelligent Computer Mathematics Christoph Benzmüller, Bruce Miller, 2020-07-17 This book constitutes the refereed proceedings of the 13th International Conference on Intelligent Computer Mathematics, CICM 2020, held in Bertinoro, Italy, in July 2020*. The 15 full papers, 1 invited paper and 2 abstracts of invited papers presented were carefully reviewed and selected from a total of 35 submissions. The papers focus on advances in automated theorem provers and formalization, computer algebra systems and their libraries, and applications of machine learning, among other topics. * The conference was held virtually due to the COVID-19 pandemic. |
| boolean pythagorean triples problem: Handbook of Satisfiability A. Biere, H. van Maaren, 2021-05-05 Propositional logic has been recognized throughout the centuries as one of the cornerstones of reasoning in philosophy and mathematics. Over time, its formalization into Boolean algebra was accompanied by the recognition that a wide range of combinatorial problems can be expressed as propositional satisfiability (SAT) problems. Because of this dual role, SAT developed into a mature, multi-faceted scientific discipline, and from the earliest days of computing a search was underway to discover how to solve SAT problems in an automated fashion. This book, the Handbook of Satisfiability, is the second, updated and revised edition of the book first published in 2009 under the same name. The handbook aims to capture the full breadth and depth of SAT and to bring together significant progress and advances in automated solving. Topics covered span practical and theoretical research on SAT and its applications and include search algorithms, heuristics, analysis of algorithms, hard instances, randomized formulae, problem encodings, industrial applications, solvers, simplifiers, tools, case studies and empirical results. SAT is interpreted in a broad sense, so as well as propositional satisfiability, there are chapters covering the domain of quantified Boolean formulae (QBF), constraints programming techniques (CSP) for word-level problems and their propositional encoding, and satisfiability modulo theories (SMT). An extensive bibliography completes each chapter. This second edition of the handbook will be of interest to researchers, graduate students, final-year undergraduates, and practitioners using or contributing to SAT, and will provide both an inspiration and a rich resource for their work. Edmund Clarke, 2007 ACM Turing Award Recipient: SAT solving is a key technology for 21st century computer science. Donald Knuth, 1974 ACM Turing Award Recipient: SAT is evidently a killer app, because it is key to the solution of so many other problems. Stephen Cook, 1982 ACM Turing Award Recipient: The SAT problem is at the core of arguably the most fundamental question in computer science: What makes a problem hard? |
| boolean pythagorean triples problem: AI Verification Guy Avni, |
| boolean pythagorean triples problem: Tools and Algorithms for the Construction and Analysis of Systems Sriram Sankaranarayanan, Natasha Sharygina, 2023-04-21 This open access book constitutes the proceedings of the 29th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2023, which was held as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2023, during April 22-27, 2023, in Paris, France. The 56 full papers and 6 short tool demonstration papers presented in this volume were carefully reviewed and selected from 169 submissions. The proceedings also contain 1 invited talk in full paper length, 13 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, flexibility, and efficiency of tools and algorithms for building computer-controlled systems. |
| boolean pythagorean triples problem: The New Mathematical Coloring Book Alexander Soifer, |
| boolean pythagorean triples problem: Automated Technology for Verification and Analysis Yu-Fang Chen, Chih-Hong Cheng, Javier Esparza, 2019-10-21 This book constitutes the refereed proceedings of the 17th International Symposium on Automated Technology for Verification and Analysis, ATVA 2019, held in Taipei, Taiwan in October 2019. The 24 regular papers presented together with 3 tool papers were carefully reviewed and selected from 65 submissions. The symposium is dedicated to the promotion of research on theoretical and practical aspects of automated analysis, verification and synthesis by providing a forum for interaction between the regional and the international research communities and industry in the field. The papers focus on cyber-physical systems; runtime techniques; testing; automata; synthesis; stochastic systems and model checking. |
| boolean pythagorean triples problem: 99 Variations on a Proof Philip Ording, 2019-01-22 An exploration of mathematical style through 99 different proofs of the same theorem This book offers a multifaceted perspective on mathematics by demonstrating 99 different proofs of the same theorem. Each chapter solves an otherwise unremarkable equation in distinct historical, formal, and imaginative styles that range from Medieval, Topological, and Doggerel to Chromatic, Electrostatic, and Psychedelic. With a rare blend of humor and scholarly aplomb, Philip Ording weaves these variations into an accessible and wide-ranging narrative on the nature and practice of mathematics. Inspired by the experiments of the Paris-based writing group known as the Oulipo—whose members included Raymond Queneau, Italo Calvino, and Marcel Duchamp—Ording explores new ways to examine the aesthetic possibilities of mathematical activity. 99 Variations on a Proof is a mathematical take on Queneau’s Exercises in Style, a collection of 99 retellings of the same story, and it draws unexpected connections to everything from mysticism and technology to architecture and sign language. Through diagrams, found material, and other imagery, Ording illustrates the flexibility and creative potential of mathematics despite its reputation for precision and rigor. Readers will gain not only a bird’s-eye view of the discipline and its major branches but also new insights into its historical, philosophical, and cultural nuances. Readers, no matter their level of expertise, will discover in these proofs and accompanying commentary surprising new aspects of the mathematical landscape. |
Boolean algebra - Wikipedia
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and …
What is a Boolean? - Computer Hope
Jun 1, 2025 · In computer science, a boolean or bool is a data type with two possible values: true or false. It is named after the English mathematician and logician George Boole, whose …
BOOLEAN Definition & Meaning - Merriam-Webster
The meaning of BOOLEAN is of, relating to, or being a logical combinatorial system (such as Boolean algebra) that represents symbolically relationships (such as those implied by the …
How Boolean Logic Works - HowStuffWorks
May 22, 2024 · A subsection of mathematical logic, Boolean logic deals with operations involving the two Boolean values: true and false. Although Boolean logic dates back to the mid-19th …
Boolean Algebra - GeeksforGeeks
Apr 15, 2025 · Boolean Algebra is a branch of algebra that deals with boolean values—true and false. It is fundamental to digital logic design and computer science, providing a mathematical …
What Boolean Logic Is & How It’s Used In Programming
Mar 21, 2022 · Boolean logic is a type of algebra in which results are calculated as either TRUE or FALSE (known as truth values or truth variables). Instead of using arithmetic operators like …
What is Boolean in computing? – TechTarget Definition
Nov 7, 2022 · In computing, the term Boolean means a result that can only have one of two possible values: true or false. Boolean logic takes two statements or expressions and applies a …
Boolean Algebra - Math is Fun
Boolean Algebra is about true and false and logic. The simplest thing we can do is to "not" or "invert": We can write this down in a "truth table" (we use T for true and F for false): We can …
Boolean - Wikipedia
Any kind of logic, function, expression, or theory based on the work of George Boole is considered Boolean. Related to this, "Boolean" may refer to: Boolean circuit, a mathematical model for …
What Is a Boolean Search? - Lifewire
Jun 12, 2023 · Boolean searches use operators (AND, OR, NOT) to help you get better results. Learn what it means and how to do a Boolean web search.
Boolean algebra - Wikipedia
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and …
What is a Boolean? - Computer Hope
Jun 1, 2025 · In computer science, a boolean or bool is a data type with two possible values: true or false. It is named after the English mathematician and logician George Boole, whose …
BOOLEAN Definition & Meaning - Merriam-Webster
The meaning of BOOLEAN is of, relating to, or being a logical combinatorial system (such as Boolean algebra) that represents symbolically relationships (such as those implied by the …
How Boolean Logic Works - HowStuffWorks
May 22, 2024 · A subsection of mathematical logic, Boolean logic deals with operations involving the two Boolean values: true and false. Although Boolean logic dates back to the mid-19th …
Boolean Algebra - GeeksforGeeks
Apr 15, 2025 · Boolean Algebra is a branch of algebra that deals with boolean values—true and false. It is fundamental to digital logic design and computer science, providing a mathematical …
What Boolean Logic Is & How It’s Used In Programming
Mar 21, 2022 · Boolean logic is a type of algebra in which results are calculated as either TRUE or FALSE (known as truth values or truth variables). Instead of using arithmetic operators like …
What is Boolean in computing? – TechTarget Definition
Nov 7, 2022 · In computing, the term Boolean means a result that can only have one of two possible values: true or false. Boolean logic takes two statements or expressions and applies …
Boolean Algebra - Math is Fun
Boolean Algebra is about true and false and logic. The simplest thing we can do is to "not" or "invert": We can write this down in a "truth table" (we use T for true and F for false): We can …
Boolean - Wikipedia
Any kind of logic, function, expression, or theory based on the work of George Boole is considered Boolean. Related to this, "Boolean" may refer to: Boolean circuit, a mathematical model for …
What Is a Boolean Search? - Lifewire
Jun 12, 2023 · Boolean searches use operators (AND, OR, NOT) to help you get better results. Learn what it means and how to do a Boolean web search.
