New discoveries about algorithms are leading scientists beyond the Church-Turing Thesis, which governs the "algorithmic universe" and asserts the conventionality of recursive algorithms. A new paradigm for computation, the super-recursive algorithm, offers promising prospects for algorithms of much greater computing power and efficiency.
Super-Recursive Algorithms provides an accessible, focused examination of the theory of super-recursive algorithms and its ramifications for the computer industry, networks, artificial intelligence, embedded systems, and the Internet. The book demonstrates how these algorithms are more appropriate as mathematical models for modern computers, and how these algorithms present a better framework for computing methods in such areas as numerical analysis, array searching, and controlling and monitoring systems. In addition, a new practically-oriented perspective on the theory of algorithms, computation, and automata, as a whole, is developed. Problems of efficiency, software development, parallel and distributed processing, pervasive and emerging computation, computer architecture, machine learning, brain modeling, knowledge discovery, and intelligent systems are addressed.
Topics and Features:
* Encompasses and systematizes all main classes of super-recursive algorithms and the theory behind them
* Describes the strengthening link between the theory of super-recursive algorithms and actual algorithms close to practical realization
* Examines the theory's basis as a foundation for advancements in computing, information science, and related technologies
* Encompasses and systematizes all main types of mathematical models of algorithms
* Highlights how super-recursive algorithms pave the way for more advanced design, utilization, and maintenance of computers
* Examines and restructures the existing variety of mathematical models of complexity of algorithms and computation, introducing new models
* Possesses a comprehensive bibliography and index
This clear exposition, motivated by numerous examples and illustrations, serves to develop a new paradigm for complex, high-performance computing based on both partial recursive functions and more inclusive recursive algorithms. Researchers and advanced students interested in theory of computation and algorithms will find the book an essential resource for an important new class of algorithms.
From the reviews:
"This book provides an examination of the theory of super-recursive algorithms and its ramifications for the computer industry, networks, artificial intelligence, embedded systems, and the Internet. ... The exposition of the book is motivated by numerous examples and illustrations. It serves to develop a new paradigm for complex, high-performance computing based on both partial recursive functions and more inclusive recursive algorithms." (Vilmar Trevisan, Zentralblatt MATH, Vol. 1070, 2005)
"This important, exciting book synthesizes all ... isolated `heresies' from the journal literature into a new, lively, coherent discipline. Beyond obvious interest to mathematicians and computer scientists, the book should attract physicists and philosophers. ... Chapters here on recursive and even subrecursive algorithms provide background and context sufficient to render this book reasonably self-contained. Summing Up: Highly recommended. General readers; lower-division undergraduates through professionals." (D. V. Feldman, CHOICE, Vol. 42 (11), July, 2005)
"This new book by Mark Burgin, Super-recursive algorithms, covers a wide variety of computational models. ... I can say that reading the book gives pleasure to the reader interested in understanding what is going on in the so-called hypercomputation community. ... the book might also be interesting from the point of view of the philosophy of computational science. ... The book provides valuable information ... ." (Jose Felix Costa, Mathematical Reviews, Issue 2008 f)