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Super-Recursive Algorithms (Monographs in Computer Science)

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This book introduces the new realm of superrecursive algorithms and the development of mathematical models for them. Although many still believe that only recursive algorithms exist and that only some of them are realizable, there are many situations in which people actually work with superrecursive algorithms. Examples of models for superrecursive algorithms are abstract automata like inductive Turing machines as well as computational schemes like limiting recursive functions.

The newly emerging field of the theory of superrecursive algorithms belongs to both mathematics and computer science. It gives a glimpse into the future of computers, networks (such as the Internet), and other devices for information interchange, processing, and production. In addition, superrecursive algorithms provide more adequate models for modern computers, the Internet, and embedded systems. Consequently, we hope (and expect) that this theory of superrecursive algorithms will, in the end, provide new insight and different perspectives on the utilization of computers, software, and the Internet.

The first goal of this book is to explain how superrecursive algorithms open new kinds of possibilities for information technology. This is an urgent task. As Papadopoulos (2002) writes, “If we don’t rethink the way we design computers, if we don’t find new ways of reasoning about distributed systems, we may find ourselves eating sand when the next wave hits.” We believe that a theory of superrecursive algorithms makes it possible to introduce a new paradigm for computation, one that yields better insight into future functioning of computers and networks. This form of computation will eclipse the more familiar kinds and will be commercially available before exotic technologies such as DNA and quantum computing arrive.

Another goal of this book is to explain how mathematics has explicated and evaluated computational possibilities and its role in extending the boundaries of computation. As we do this, we will present the theory of algorithms and computation in a new, more organized structure.
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