Lattice Functions And Equations

Author: Sergiu Rudeanu
Publisher: Springer Science & Business Media
ISBN: 144710241X
Size: 19.20 MB
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One of the chief aims of this self-contained monograph is to survey recent developments of Boolean functions and equations, as well as lattice functions and equations in more general classes of lattices. Lattice (Boolean) functions are algebraic functions defined over an arbitrary lattice (Boolean algebra), while lattice (Boolean) equations are equations expressed in terms of lattice (Boolean) functions. Special attention is also paid to consistency conditions and reproductive general solutions. Applications refer to graph theory, automata theory, synthesis of circuits, fault detection, databases, marketing and others. Lattice Functions and Equations updates and extends the author's previous monograph - Boolean Functions and Equations.

Lattice Functions And Equations

Author: Sergiu Rudeanu
Publisher: Springer Science & Business Media
ISBN: 144710241X
Size: 16.38 MB
Format: PDF, Kindle
View: 3771
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One of the chief aims of this self-contained monograph is to survey recent developments of Boolean functions and equations, as well as lattice functions and equations in more general classes of lattices. Lattice (Boolean) functions are algebraic functions defined over an arbitrary lattice (Boolean algebra), while lattice (Boolean) equations are equations expressed in terms of lattice (Boolean) functions. Special attention is also paid to consistency conditions and reproductive general solutions. Applications refer to graph theory, automata theory, synthesis of circuits, fault detection, databases, marketing and others. Lattice Functions and Equations updates and extends the author's previous monograph - Boolean Functions and Equations.

Modeling Decisions For Artificial Intelligence

Author: Vicenç Torra
Publisher: Springer Science & Business Media
ISBN: 3642162916
Size: 48.70 MB
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This volume contains papers presented at the 7th International Conference on Modeling Decisions for Arti?cial Intelligence (MDAI 2010), held in Perpignan, France, October 27–29. This conference followed MDAI 2004 (Barcelona, C- alonia, Spain), MDAI 2005 (Tsukuba, Japan), MDAI 2006 (Tarragona, Cata- nia, Spain), MDAI 2007 (Kitakyushu, Japan), MDAI 2008 (Sabadell, Catalonia, Spain), and MDAI 2009 (Awaji Island, Japan) with proceedings also published in the LNAI series (Vols. 3131, 3558, 3885, 4617, 5285, and 5861). The aim of this conference was to provide a forum for researchers to discuss theory and tools for modeling decisions, as well as applications that encompass decision-making processes and information fusion techniques. The organizers received 43 papers from 12 di?erent countries, from Europe, Asia, Australia and Africa, 25 of which are published in this volume. Each s- mission received at least two reviews from the Program Committee and a few externalreviewers.Wewouldliketoexpressourgratitudetothemfortheirwork. The plenary talks presented at the conference are also included in this volume. TheconferencewassupportedbytheCNRS:CentreNationaldelaRecherche Scienti?que,theUniversit´ edePerpignanVia Domitia,theELIAUS:Laboratoire Electronique Informatique Automatique Syst` emes, IMERIR: Ecole d'Ing´ enierie Informatique et Robotique, the UNESCO Chair in Data Privacy, the Japan - cietyforFuzzyTheoryandIntelligentInformatics(SOFT),theCatalanAssoc- tionfor Arti?cialIntelligence(ACIA), the EuropeanSociety for Fuzzy Logicand Technology(EUSFLAT), the Spanish MEC(ARES—CONSOLIDER INGENIO 2010 CSD2007-00004).

Advanced Discrete Mathematics

Author: UDAY SINGH RAJPUT
Publisher: PHI Learning Pvt. Ltd.
ISBN: 8120345894
Size: 23.93 MB
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Written in an accessible style, this text provides a complete coverage of discrete mathematics and its applications at an appropriate level of rigour. The book discusses algebraic structures, mathematical logic, lattices, Boolean algebra, graph theory, automata theory, grammars and recurrence relations. It covers the important topics such as coding theory, Dijkstra’s shortest path algorithm, reverse polish notation, Warshall’s algorithm, Menger’s theorem, Turing machine, and LR(k) parsers, which form a part of the fundamental applications of discrete mathematics in computer science. In addition, Pigeonhole principle, ring homomorphism, field and integral domain, trees, network flows, languages, and recurrence relations. The text is supported with a large number of examples, worked-out problems and diagrams that help students understand the theoretical explanations. The book is intended as a text for postgraduate students of mathematics, computer science, and computer applications. In addition, it will be extremely useful for the undergraduate students of computer science and engineering.

Discrete Computational Structures

Author: Robert R. Korfhage
Publisher: Academic Press
ISBN: 1483264297
Size: 27.62 MB
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Discrete Computational Structures describes discrete mathematical concepts that are important to computing, covering necessary mathematical fundamentals, computer representation of sets, graph theory, storage minimization, and bandwidth. The book also explains conceptual framework (Gorn trees, searching, subroutines) and directed graphs (flowcharts, critical paths, information network). The text discusses algebra particularly as it applies to concentrates on semigroups, groups, lattices, propositional calculus, including a new tabular method of Boolean function minimization. The text emphasizes combinatorics and probability. Examples show different techniques of the general process of enumerating objects. Combinatorics cover permutations, enumerators for combinations, Stirling numbers, cycle classes of permutations, partitions, and compositions. The book cites as example the interplay between discrete mathematics and computing using a system of distinct representatives (SDR) problem. The problem, originating from group theory, graph theory, and set theory can be worked out by the student with a network model involving computers to generate and analyze different scenarios. The book is intended for sophomore or junior level, corresponding to the course B3, "Introduction to Discrete Structures," in the ACM Curriculum 68, as well as for mathematicians or professors of computer engineering and advanced mathematics.

Newsletter

Author: New Zealand Mathematical Society
Publisher:
ISBN:
Size: 16.46 MB
Format: PDF, ePub
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Theory Of Linear And Integer Programming

Author: Alexander Schrijver
Publisher: John Wiley & Sons
ISBN: 9780471982326
Size: 67.66 MB
Format: PDF, Docs
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Theory of Linear and Integer Programming Alexander Schrijver Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands This book describes the theory of linear and integer programming and surveys the algorithms for linear and integer programming problems, focusing on complexity analysis. It aims at complementing the more practically oriented books in this field. A special feature is the author's coverage of important recent developments in linear and integer programming. Applications to combinatorial optimization are given, and the author also includes extensive historical surveys and bibliographies. The book is intended for graduate students and researchers in operations research, mathematics and computer science. It will also be of interest to mathematical historians. Contents 1 Introduction and preliminaries; 2 Problems, algorithms, and complexity; 3 Linear algebra and complexity; 4 Theory of lattices and linear diophantine equations; 5 Algorithms for linear diophantine equations; 6 Diophantine approximation and basis reduction; 7 Fundamental concepts and results on polyhedra, linear inequalities, and linear programming; 8 The structure of polyhedra; 9 Polarity, and blocking and anti-blocking polyhedra; 10 Sizes and the theoretical complexity of linear inequalities and linear programming; 11 The simplex method; 12 Primal-dual, elimination, and relaxation methods; 13 Khachiyan's method for linear programming; 14 The ellipsoid method for polyhedra more generally; 15 Further polynomiality results in linear programming; 16 Introduction to integer linear programming; 17 Estimates in integer linear programming; 18 The complexity of integer linear programming; 19 Totally unimodular matrices: fundamental properties and examples; 20 Recognizing total unimodularity; 21 Further theory related to total unimodularity; 22 Integral polyhedra and total dual integrality; 23 Cutting planes; 24 Further methods in integer linear programming; Historical and further notes on integer linear programming; References; Notation index; Author index; Subject index

Applied Algebra And Number Theory

Author: Gerhard Larcher
Publisher: Cambridge University Press
ISBN: 1107074002
Size: 78.51 MB
Format: PDF
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