Galois Connections and Fixed Point Calculus
by Roland Backhouse
Number of pages: 105
Recursion is a very powerful problem-solving technique that is used widely in computing science. It is used, for example, in the definition of programming languages, as a fundamental programming structure in functional and logic programming, and in the definition of data structures. A complete understanding of recursion can only be achieved by studying its algebraic properties. This tutorial covers fixed point calculus, which is about the solution of recursive equations defined by a monotonic endofunction on a partially ordered set. It presents the basic theory of fixed point calculus together with a number of applications of direct relevance to the construction of computer programs. The tutorial also presents the theory and application of Galois connections between partially ordered sets. In particular, the intimate relation between Galois connections and fixed point equations is amply demonstrated.
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by V. E. Wolfengagen - JurInfoR
This work covers the advanced topics in main ideas of computing in general. Material is especially useful for the instructor, postgraduate and graduate students of IT-specialties and is suitable for the system of training of specialists.
by Christian P. Robert - arXiv
We will first present the most standard computational challenges met in Bayesian Statistics, focusing primarily on mixture estimation and on model choice issues, and then relate these problems with computational solutions.
by Eitan Gurari - Computer Science Pr
The book explores questions and terminologies concerning programs, computers, and computation. The exploration reduces to a study of mathematical theories, such as those of automata and formal languages, theories interesting in their own right.
by David Evans - University of Virginia
An introduction to the most important ideas in computing. It focuses on how to describe information processes by defining procedures, how to analyze the costs required to carry out a procedure, and the limits of what can be computed mechanically.