Introduction to Lattice Theory with Computer Science Applications

Beschreibung

A computational perspective on partial order and lattice theory, focusing on algorithms and their applications This book provides a uniform treatment of the theory and applications of lattice theory. The applications covered include tracking dependency in distributed systems, combinatorics, detecting global predicates in distributed systems, set families, and integer partitions. The book presents algorithmic proofs of theorems whenever possible. These proofs are written in the calculational style advocated by Dijkstra, with arguments explicitly spelled out step by step. The author's intent is for readers to learn not only the proofs, but the heuristics that guide said proofs. Introduction to Lattice Theory with Computer Science Applications: * Examines; posets, Dilworth's theorem, merging algorithms, lattices, lattice completion, morphisms, modular and distributive lattices, slicing, interval orders, tractable posets, lattice enumeration algorithms, and dimension theory * Provides end of chapter exercises to help readers retain newfound knowledge on each subject * Includes supplementary material at www.ece.utexas.edu/~garg Introduction to Lattice Theory with Computer Science Applications is written for students of computer science, as well as practicing mathematicians.

Autor*in

Vijay K. Garg

Themen in »Introduction to Lattice Theory with Computer Science Applications«

Computer Science Electrical & Electronics Engineering Elektrotechnik u. Elektronik Informatik Numerical Methods & Algorithms Numerische Methoden u. Algorithmen Parallel and Distributed Computing Paralleles u. Verteiltes Rechnen Verbandstheorie

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"This nice book on lattices and their applications in computer science is written fromthe perspective of a computer scientist rather than a mathematician...Given its emphasis on algorithms and their complexity, itseems to be mainly intended for students of computer science and engineering. Theauthor's approach is based on the premise that a student needs to learn the heuristicsthat guide the proofs, besides the proofs themselves, and to learn ways to extend andanalyze theorems...One of the most important and valuable features of the book is its focus on applicationsof lattice theory. The author intends to treat applications on par with the theory." Altogether a "lovely book". (Mathematical Reviews/MathSciNet April 2017)
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