The Calculus of Computation

Computational logic is a fast-growing field with applications in artificial intelligence, constraint solving, and the design and verification of software and hardware systems. Written with graduate and advanced undergraduate students in mind, this textbook introduces computational logic from the foundations of first-order logic to state-of-the-art decision procedures for arithmetic, data structures, and combination theories.

This book is a comprehensive, unifying introduction to the field of mathematical analysis and the mathematics of computing. It develops the relevant theory at a modern level and it directly relates modern mathematical ideas to their diverse applications.

This book is a comprehensive, unifying introduction to the field of mathematical analysis and the mathematics of computing. It develops the relevant theory at a modern level and it directly relates modern mathematical ideas to their diverse applications.

Hypercomputation is a relatively new theory of computation which treats computing methods and devices that transcend the Church-Turing thesis. This book will provide a thorough description of the field of hypercomputation, covering all attempts at devising conceptual hypermachines and all new promising computational paradigms that may eventually lead to the construction of a hypermachine.

In this volume we will present some applications of special functions in computer science. This largely consists of adaptations of articles that have appeared in the literature . Here they are presented in a format made accessible for the non-expert by providing some context. The material on group representations and Young tableaux is introductory in nature. However, the algebraic approach of Chapter 2 is original to the authors and has not appeared previously . Similarly, the material and approach based on Appell states, so formulated, is presented here for the first time . As in all volumes of this series, this one is suitable for self-study by researchers . It is as well appropriate as a text for a course or advanced seminar . The solutions are tackled with the help of various analytical techniques, such as g- erating functions, and probabilistic methods/insights appear regularly . An interesting feature is that, as has been the case in classical applications to physics, special functions arise- here in complexity analysis. And, as in physics, their appearance indicates an underlying Lie structure. Our primary audience is applied mathematicians and theoretical computer scientists . We are quite sure that pure mathematicians will find this volume interesting and useful as well .