Singh A. Elements of Computation Theory

Издательство Springer, 2009, -428 pp.

The foundation of computer science is built upon the following questions:
What is an algorithm?
What can be computed and what cannot be computed?
What does it mean for a function to be computable?
How does computational power depend upon programming constructs?
Which algorithms can be considered feasible?
For more than 70 years, computer scientists are searching for answers to such questions. Their ingenious techniques used in answering these questions form the theory of computation.
Theory of computation deals with the most fundamental ideas of computer science in an abstract but easily understood form. The notions and techniques employed are widely spread across various topics and are found in almost every branch of computer science. It has thus become more than a necessity to revisit the foundation, lea the techniques, and apply them with confidence.
This book is about this solid, beautiful, and pervasive foundation of computer science. It introduces the fundamental notions, models, techniques, and results that form the basic paradigms of computing. It gives an introduction to the concepts and mathematics that computer scientists of our day use to model, to argue about, and to predict the behavior of algorithms and computation. The topics chosen here have shown remarkable persistence over the years and are very much in current use. The book realizes the following goals:
To introduce to the students of computer science and mathematics the elegant and useful models and abstractions that have been created over the years for solving foundational problems about computation
To help the students develop the ability to form abstract models of their own and to reason about them
To strengthen the students’ capability for carrying out formal and rigorous arguments about algorithms
To equip the students with the knowledge of the computational procedures that have hunted our predecessors, so that they can identify similar problems and structures whenever they encounter one
To make the essential elements of the theory of computation accessible to notso- matured students having not much mathematical background, in a way that is mathematically uncompromising
To make the students realize that mathematical rigour in arguing about algorithms can be very attractive
To keep in touch with the foundations as computer science has become a much more matured and established discipline

Mathematical Preliminaries
Regular Languages
Equivalences
Structure of Regular Languages
Context-free Languages
Structure of CFLs
Computably Enumerable Languages
A Noncomputably Enumerable Language
Algorithmic Solvability
Computational Complexity