Computability & Unsolvability

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Courier Corporation, 1958 - 248 ページ
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"A clearly written, well-presented survey of an intriguing subject." — Scientific American. Classic text considers general theory of computability, computable functions, operations on computable functions, Turing machines self-applied, unsolvable decision problems, applications of general theory, mathematical logic, Kleene hierarchy, computable functionals, classification of unsolvable decision problems and more.
 

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目次

COMPUTABLE FUNCTIONS
3
OPERATIONS ON COMPUTABLE FUNCTIONS
25
RECURSIVE FUNCTIONS
41
TURING MACHINES SELFAPPLIED
56
UNSOLVABLE DECISION PROBLEMS
66
APPLICATIONS OF THE GENERAL THEORY
79
COMBINATORIAL PROBLEMS
81
DIOPHANTINE EQUATIONS
102
MATHEMATICAL LOGIC
117
FURTHER DEVELOPMENT OF THE GENERAL THEORY
143
THE KLEENE HIERARCHY
145
COMPUTABLE FUNCTIONALS
162
THE CLASSIFICATION OF UNSOLVABLE DECISION PROBLEMS
179
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著者について (1958)

Martin Davis: Computer Science Pioneer
Dover's publishing relationship with Martin Davis, now retired from NYU and living in Berkeley, goes back to 1985 when we reprinted his classic 1958 book Computability and Unsolvability, widely regarded as a classic of theoretical computer science. A graduate of New York's City College, Davis received his PhD from Princeton in the late 1940s and became one of the first computer programmers in the early 1950s, working on the ORDVAC computer at The University of Illinois. He later settled at NYU where he helped found the Computer Science Department.

Not many books from the infancy of computer science are still alive after several decades, but Computability and Unsolvability is the exception. And The Undecidable is an anthology of fundamental papers on undecidability and unsolvability by major figures in the field including Godel, Church, Turing, Kleene, and Post.

Critical Acclaim for Computability and Unsolvability:
"This book gives an expository account of the theory of recursive functions and some of its applications to logic and mathematics. It is well written and can be recommended to anyone interested in this field. No specific knowledge of other parts of mathematics is presupposed. Though there are no exercises, the book is suitable for use as a textbook." — J. C. E. Dekker, Bulletin of the American Mathematical Society, 1959

Critical Acclaim for The Undecidable:
"A valuable collection both for original source material as well as historical formulations of current problems." — The Review of Metaphysics

"Much more than a mere collection of papers . . . a valuable addition to the literature." — Mathematics of Computation

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