Relational Topology

This book introduces and develops new algebraic methods to work with relations, often conceived as Boolean matrices, and applies them to topology. Although these objects mirror the matrices that appear throughout mathematics, numerics, statistics, engineering, and elsewhere, the methods used to work with them are much less well known. In addition to their purely topological applications, the volume also details how the techniques may be successfully applied to spatial reasoning and to logics of computer science. Topologists will find several familiar concepts presented in a concise and algebraically manipulable form which is far more condensed than usual, but visualized via represented relations and thus readily graspable. This approach also offers the possibility of handling topological problems using proof assistants.

This book constitutes the thoroughly refereed post-conference proceedings of the 13th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 13, held in Cambridge, UK, in September 2012. The 23 revised full papers presented were carefully selected from 39 submissions in the general area of relational and algebraic methods in computer science, adding special focus on formal methods for software engineering, logics of programs and links with neighboring disciplines. The papers are structured in specific fields on applications to software specification and correctness, mechanized reasoning in relational algebras, algebraic program derivation, theoretical foundations, relations and algorithms, and properties of specialized relations.

This book constitutes the proceedings of the 16th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2017, held in Lyon, France, in May 2017. The 17 revised full papers and 2 invited papers presented together with 1 invited abstract were carefully selected from 28 submissions. Topics covered range from mathematical foundations to applications as conceptual and methodological tools in computer science and beyond.

CAD84: 6th International Conference and Exhibition on Computers in Design Engineering is a collection of 64 conference papers that covers a wide range of topics on computer-aided design (CAD) and CADCAM, including CAD process plant designs, techniques, drafting systems, electronics, geometric design, kinematics, mechanical engineering, solid modelling, and structures. The book starts by describing the progress that has been made in hardware and software. The text continues by presenting papers about interactive system for the design and production of computer programs; an algorithmic language for the definition and manipulation of drawings; and a software tool to enable application dialog input to be developed for new or existing programs with or without problem-oriented language. Papers on the design of a drawing system that consists of a language kernel for tailoring the system to support various styles and practices and on an automated drawing and cost estimation program for platform frame construction named HOUSE24 are also presented. The book also discusses HILO-2, which is a single coherent system for design verification, fault simulation, and test vector generation. The text will benefit both students and professionals using CAD.

This introductory text covers the algebra of subsets and of rings and fields of sets, complementation and ideal theory in the distributive lattice, closure function, neighborhood topology, much more. Includes numerous exercises. 1960 edition.

This book constitutes the refereed proceedings of the 8th International Symposium on Spatial and Temporal Databases, SSTD 2003, held at Santorini Island, Greece in July 2003. The 28 revised full papers presented together with a keynote paper were carefully reviewed and selected from 105 submissions. the papers are organized in topical sections on access methods, advanced query processing, data mining and data warehousing, distance-based queries, mobility and moving points management, modeling and languages, similarity processing, systems and implementation issues.

This book constitutes the proceedings of the 20th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2023, which took place in Augsburg, Germany, during April 3–6, 2023. The 17 papers presented in this book were carefully reviewed and selected from 26 submissions. They deal with the development and dissemination of relation algebras, Kleene algebras, and similar algebraic formalisms. Topics covered range from mathematical foundations to applications as conceptual and methodological tools in computer science and beyond. Apart from the submitted articles, this volume features the abstracts of the presentations of the three invited speakers.