In the 1930s a series of seminal works published by Alan Turing, Kurt Gödel, Alonzo Church, and others established the theoretical basis for computability. This work, advancing precise characterizations of effective, algorithmic computability, was the culmination of intensive investigations into the foundations of mathematics. In the...

The theory of computing provides computer science with concepts, models, and formalisms for reasoning about both the resources needed to carry out computations and the efficiency of the computations that use these resources. It provides tools to measure the difficulty of combinatorial problems both absolutely and in comparison with other...

"This is an impressive book. The subject has been thoroughly researched and carefully presented. All the machine models central to the modern theory of...

Logic is sometimes called the foundation of mathematics: the logician studies the kinds of reasoning used in the individual steps of a proof. Alonzo Church was a pioneer in the field of mathematical logic, whose contributions to number theory and the theories of algorithms and computability laid the theoretical foundations of computer...

The two main themes of this book, logic and complexity, are both essential for understanding the main problems about the foundations of mathematics. Logical Foundations of Mathematics and Computational Complexity covers a broad spectrum of results in logic and set theory that are relevant to the foundations, as well as the results in...

Computability has played a crucial role in mathematics and computer science – leading to the discovery, understanding and classification of decidable/ undecidable problems, paving the way to the modern computer era and affecting deeply our view of the world. Recent new paradigms of computation, based on biological and physical...