The
Pillars of Computation Theory
State, Encoding, Nondeterminism
Rosenberg, Arnold L.
creator
author.
SpringerLink (Online service)
text
xxu
2010
First.
monographic
eng
access
XVIII, 326 p. 49 illus. online resource.
Computation theory is a discipline that strives to use mathematical tools and concepts in order to expose the nature of the activity that we call “computation” and to explain a broad range of observed computational phenomena. Why is it harder to perform some computations than others? Are the differences in difficulty that we observe inherent, or are they artifacts of the way we try to perform the computations? Even more basically: how does one reason about such questions? This book strives to endow upper-level undergraduate students and lower-level graduate students with the conceptual and manipulative tools necessary to make Computation theory part of their professional lives. The author tries to achieve this goal via three stratagems that set this book apart from most other texts on the subject. (1) The author develops the necessary mathematical concepts and tools from their simplest instances, so that the student has the opportunity to gain operational control over the necessary mathematics. (2) He organizes the development of the theory around the three “pillars” that give the book its name, so that the student sees computational topics that have the same intellectual origins developed in physical proximity to one another. (3) He strives to illustrate the “big ideas” that computation theory is built upon with applications of these ideas within “practical” domains that the students have seen elsewhere in their courses, in mathematics, in computer science, and in computer engineering.
PROLEGOMENA -- Mathematical Preliminaries -- STATE -- Online Automata: Exemplars of #x201C;State#x201D; -- Finite Automata and Regular Languages -- Applications of the Myhill#x2013;Nerode Theorem -- Enrichment Topics -- ENCODING -- Countability and Uncountability: The Precursors of #x201C;Encoding#x201D; -- Enrichment Topic: #x201C;Efficient#x201D; Pairing Functions, with Applications -- Computability Theory -- NONDETERMINISM -- Nondeterministic Online Automata -- Nondeterministic FAs -- Nondeterminism in Computability Theory -- Complexity Theory.
by Arnold L. Rosenberg.
Computer science
Computers
Algorithms
Mathematical logic
Computer science
Mathematics
Computer Science
Theory of Computation
Mathematics of Computing
Algorithm Analysis and Problem Complexity
Mathematical Logic and Foundations
Computation by Abstract Devices
Mathematical Logic and Formal Languages
QA75.5-76.95
004.0151
Springer eBooks
Universitext
9780387096391
http://dx.doi.org/10.1007/978-0-387-09639-1
http://dx.doi.org/10.1007/978-0-387-09639-1
100301
20180115171345.0
978-0-387-09639-1