January 2011
Intermediate to advanced
192 pages
5h 34m
English
Content preview from Computability Theory
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Foreword
The study of the class of computable partial functions (i.e., recursive partial functions)
stands at the intersection of three fields: mathematics, theoretical computer science,
and philosophy.
l
Mathematically, computability theory originates from the concept of an algorithm.
It leads to a classification of functions according their inherent complexity.
l
For the computer scientist, computability theory shows that quite apart from prac-
tical matters of running time and memory space, there is a purely theoretical limit
to what computer programs can do. This is an important fact, and leads to the ques-
tions: Where is the limit? What is on this side of the limit, and what lies beyond it?
l
Computability is relevant to the philosophy of mathematics ...
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