Computation theory is a discipline that uses mathematical concepts and tools to expose the nature of "computation" and to explain a broad range of 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? How does one reason about such questions? This unique textbook strives to endow students with conceptual and manipulative tools necessary to make computation theory part of their professional lives. The work achieves this goal by means of three stratagems that set its approach apart from most other texts on the subject. For starters, it develops the necessary mathematical concepts and tools from the concepts' simplest instances, thereby helping students gain operational control over the required mathematics. Secondly, it organizes development of theory around four "pillars," enabling students to see computational topics that have the same intellectual origins in physical proximity to one another. Finally, the text illustrates the "big ideas" that computation theory is built upon with applications of these ideas within "practical" domains in mathematics, computer science, computer engineering, and even further afield. Suitable for advanced undergraduate students and beginning graduates, this textbook augments the "classical" models that traditionally support courses on computation theory with novel models inspired by "real, modern" computational topics,such as crowd-sourced computing, mobile computing, robotic path planning, and volunteer computing. Arnold L. Rosenberg is Distinguished Univ. Professor Emeritus at University of Massachusetts, Amherst, USA. Lenwood S. Heath is Professor at Virgina Tech, Blacksburg, USA.

An accessible and rigorous textbook for introducing undergraduates to computer science theory What Can Be Computed? is a uniquely accessible yet rigorous introduction to the most profound ideas at the heart of computer science. Crafted specifically for undergraduates who are studying the subject for the first time, and requiring minimal prerequisites, the book focuses on the essential fundamentals of computer science theory and features a practical approach that uses real computer programs (Python and Java) and encourages active experimentation. It is also ideal for self-study and reference. The book covers the standard topics in the theory of computation, including Turing machines and finite automata, universal computation, nondeterminism, Turing and Karp reductions, undecidability, time-complexity classes such as P and NP, and NP-completeness, including the Cook-Levin Theorem. But the book also provides a broader view of computer science and its historical development, with discussions of Turing's original 1936 computing machines, the connections between undecidability and Gödel's incompleteness theorem, and Karp's famous set of twenty-one NP-complete problems. Throughout, the book recasts traditional computer science concepts by considering how computer programs are used to solve real problems. Standard theorems are stated and proven with full mathematical rigor, but motivation and understanding are enhanced by considering concrete implementations. The book's examples and other content allow readers to view demonstrations of—and to experiment with—a wide selection of the topics it covers. The result is an ideal text for an introduction to the theory of computation. An accessible and rigorous introduction to the essential fundamentals of computer science theory, written specifically for undergraduates taking introduction to the theory of computation Features a practical, interactive approach using real computer programs (Python in the text, with forthcoming Java alternatives online) to enhance motivation and understanding Gives equal emphasis to computability and complexity Includes special topics that demonstrate the profound nature of key ideas in the theory of computation Lecture slides and Python programs are available at whatcanbecomputed.com

Computing Methodologies -- Artificial Intelligence.