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Books > Computing & IT > General theory of computing
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Turing Computability - Theory and Applications (Paperback, Softcover reprint of the original 1st ed. 2016)
Loot Price: R2,576
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Turing Computability - Theory and Applications (Paperback, Softcover reprint of the original 1st ed. 2016)
Series: Theory and Applications of Computability
Expected to ship within 10 - 15 working days
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Turing's famous 1936 paper introduced a formal definition of a
computing machine, a Turing machine. This model led to both the
development of actual computers and to computability theory, the
study of what machines can and cannot compute. This book presents
classical computability theory from Turing and Post to current
results and methods, and their use in studying the information
content of algebraic structures, models, and their relation to
Peano arithmetic. The author presents the subject as an art to be
practiced, and an art in the aesthetic sense of inherent beauty
which all mathematicians recognize in their subject. Part I gives a
thorough development of the foundations of computability, from the
definition of Turing machines up to finite injury priority
arguments. Key topics include relative computability, and
computably enumerable sets, those which can be effectively listed
but not necessarily effectively decided, such as the theorems of
Peano arithmetic. Part II includes the study of computably open and
closed sets of reals and basis and nonbasis theorems for
effectively closed sets. Part III covers minimal Turing degrees.
Part IV is an introduction to games and their use in proving
theorems. Finally, Part V offers a short history of computability
theory. The author has honed the content over decades according to
feedback from students, lecturers, and researchers around the
world. Most chapters include exercises, and the material is
carefully structured according to importance and difficulty. The
book is suitable for advanced undergraduate and graduate students
in computer science and mathematics and researchers engaged with
computability and mathematical logic.
General
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