Introduction to Lattice Theory with Computer Science Applications

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