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Lattice Functions And Equations

Author: Sergiu Rudeanu
Publisher: Springer Science & Business Media
ISBN: 144710241X
Size: 42.61 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.

Modeling Decisions For Artificial Intelligence

Author: Vicenç Torra
Publisher: Springer Science & Business Media
ISBN: 3642162916
Size: 13.75 MB
Format: PDF, Docs
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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: 28.91 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: 33.73 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.

Fundamentals Of Discrete Mathematical Structures

Author: K. R. CHOWDHARY
Publisher: PHI Learning Pvt. Ltd.
ISBN: 812035074X
Size: 20.61 MB
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This updated text, now in its Third Edition, continues to provide the basic concepts of discrete mathematics and its applications at an appropriate level of rigour. The text teaches mathematical logic, discusses how to work with discrete structures, analyzes combinatorial approach to problem-solving and develops an ability to create and understand mathematical models and algorithms essentials for writing computer programs. Every concept introduced in the text is first explained from the point of view of mathematics, followed by its relation to Computer Science. In addition, it offers excellent coverage of graph theory, mathematical reasoning, foundational material on set theory, relations and their computer representation, supported by a number of worked-out examples and exercises to reinforce the students’ skill. Primarily intended for undergraduate students of Computer Science and Engineering, and Information Technology, this text will also be useful for undergraduate and postgraduate students of Computer Applications. New to this Edition Incorporates many new sections and subsections such as recurrence relations with constant coefficients, linear recurrence relations with and without constant coefficients, rules for counting and shorting, Peano axioms, graph connecting, graph scanning algorithm, lexicographic shorting, chains, antichains and order-isomorphism, complemented lattices, isomorphic order sets, cyclic groups, automorphism groups, Abelian groups, group homomorphism, subgroups, permutation groups, cosets, and quotient subgroups. Includes many new worked-out examples, definitions, theorems, exercises, and GATE level MCQs with answers.

Logic And Random Structures

Author: Ravi Bopu Boppana
Publisher: American Mathematical Soc.
ISBN: 9780821870785
Size: 41.23 MB
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This volume contains selected papers from the DIMACS Workshop on Logic an Random Structures held in November 1995. The workshop was a major event of the DIMACS Special Year on Logic and Algorithms. The central theme was the relationship between logic and probabilistic techniques in the study of finite structures. In the last several years, this subject has developed into a very active area of mathematical logic with important connections to computer science. The DIMACS workshop was the first of its kind devoted to logic and random structures. Recent work of leaders in the field is contained in the volume, as well as new theoretical developments and applications to computer science.