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New Computational Paradigms: Changing Conceptions of What is Computable
New Computational Paradigms: Changing Conceptions of What is Computable
In recent years, classical computability has expanded beyond its original scope to address issues related to computability and complexity in algebra, analysis, and physics. The deep interconnection between "computation" and "proof" has originated much of the most significant work in constructive mathematics and mathematical...
Computability Theory: An Introduction to Recursion Theory
Computability Theory: An Introduction to Recursion Theory

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.

Mathematically, computability theory originates from the concept of an algorithm. It leads to a classification of functions according...

A Concise Introduction to Languages and Machines (Undergraduate Topics in Computer Science)
A Concise Introduction to Languages and Machines (Undergraduate Topics in Computer Science)

This book focuses on key theoretical topics of computing, in particular formal languages and abstract machines. It is intended primarily to support the theoretical modules on a computer science or computing-related undergraduate degree scheme.

Though the book is primarily theoretical in nature, it attempts to avoid the...

Computability and Complexity Theory (Texts in Computer Science)
Computability and Complexity Theory (Texts in Computer Science)

This revised and extensively expanded edition of Computability and Complexity Theory comprises essential materials that are core knowledge in the theory of computation. The book is self-contained, with a preliminary chapter describing key mathematical concepts and notations.  Subsequent chapters move from the qualitative aspects of...

Foundations of Computing
Foundations of Computing

It may sound surprising that in computing, a field which develops so fast that the future often becomes the past without having been the present, there is nothing more stable and worthwhile learning than its foundations.

It may sound less surprising that in a field with such a revolutionary methodological impact on all sciences and...

Proofs and Algorithms: An Introduction to Logic and Computability (Undergraduate Topics in Computer Science)
Proofs and Algorithms: An Introduction to Logic and Computability (Undergraduate Topics in Computer Science)

Logic is a branch of philosophy, mathematics and computer science. It studies the required methods to determine whether a statement is true, such as reasoning and computation.

Proofs and Algorithms: Introduction to Logic and Computability is an introduction to the fundamental concepts of contemporary logic - those of a
...

The Formal Semantics of Programming Languages: An Introduction (Foundations of Computing)
The Formal Semantics of Programming Languages: An Introduction (Foundations of Computing)

The Formal Semantics of Programming Languages provides the basic mathematical techniques necessary for those who are beginning a study of the semantics and logics of programming languages. These techniques will allow students to invent, formalize, and justify rules with which to reason about a variety of programming languages. Although...

From Writing to Computers
From Writing to Computers
... the broad and clear analysis of writing and language, and of automata theory, formal logic, and computability theory he uses to reach [his conclusion] is well worth reading.
–H. D. Warner, Western New England College

From Writing to Computers takes as its central theme the issue of a
...
Elementary Computability, Formal Languages, and Automata
Elementary Computability, Formal Languages, and Automata

This book is an introduction to theoretical computer science emphasizing two interrelated areas: the theory of computability {how to tell whether problems are algorithmically solvable) and the theory of formal languages (how to design and use special languages, as for algorithms). Automata {idealized computer devices) are used as precise...

Philosophy of Mathematics (Handbook of the Philosophy of Science)
Philosophy of Mathematics (Handbook of the Philosophy of Science)

One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are...

The Annotated Turing: A Guided Tour Through Alan Turing's Historic Paper on Computability and the Turing Machine
The Annotated Turing: A Guided Tour Through Alan Turing's Historic Paper on Computability and the Turing Machine

Before digital computers ever existed, Alan Turing envisioned their power and versatility...but also proved what computers could never do.

In an extraordinary and ultimately tragic life that unfolded like a novel, Turing helped break the German Enigma code to turn the tide of World War II, later speculated on...

Computational Prospects Of Infinity - Part I: Tutorials (Lecture Notes)
Computational Prospects Of Infinity - Part I: Tutorials (Lecture Notes)
This volume presents the written versions of the tutorial lectures given at the Workshop on Computational Prospects of Infinity, held from 18 June to 15 August 2005 at the Institute for Mathematical Sciences, National University of Singapore. It consists of articles by four of the leading experts in recursion theory (computability theory) and set...
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