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.

Promotes understanding through multi-faceted explanations Provides a comprehensive introduction, mapping a pillars-based organization Connects expected areas of reader interest to topics and applications

Autorentext
Prof. Arnold Rosenberg is a distinguished university professor emeritus at the University of Massachusetts, Amherst. He also held research positions at Northeastern University and Colorado State University, a professorship at Duke University, and a staff research position at IBM Watson Research Center. He was elected a fellow of the ACM in 1996 for his work on graph-theoretic models of compuation, emphasizing theoretical studies of parallel algorithms and architectures, VLSI design and layout, and data structures. In 1997, he was elected as a fellow of the IEEE for fundamental contributions to theoretical aspects of computer science and engineering. Prof. Denis Trystram is a distinguished professor at the Grenoble Institute of Engineering, an honorary member of the Institut Universitaire de France (IUF), and he works at the Laboratoire d'Informatique de Grenoble (LIG) in the team-project DataMove-INRIA. His research interestst include the design and analysis of efficient algorithms for optimizing resource use in parallel and distributed systems, approximation algorithms for scheduling and packing problems, and algorithms for data analytics. Both authors have considerable teaching and practical experience in the application of discrete mathematics approaches to computing tasks.

Inhalt

Preface.- I: Introduction.- 1 Introducing Computation Theory.- 2 Introducing the Book.- II: Pillar S: STATE.- 3 Pure State-Based Computational Models.- 4 The Myhill-Nerode Theorem: Implications and Applications.- 5 Online Turing Machines and the Implications of Online Computing.- 6 Pumping: Computational Pigeonholes in Finitary Systems.- 7 Mobility in Computing: An FA Navigates a Mesh.- 8 The Power of Cooperation: Teams of MFAs on a Mesh.- III: Pillar E: ENCODING.- 9 Countability and Uncountability: The Precursors of ENCODING .- 10 Computability Theory.- 11 A Church-Turing Zoo of Computational Models.- 12 Pairing Functions as Encoding Mechanisms.- IV: Pillar N: NONDETERMINISM.- 13 Nondeterminism as Unbounded Parallelism.- 14 Nondeterministic Finite Automata.- 15 Nondeterminism as Unbounded Search.- 16 Complexity Theory.- V: Pillar P: PRESENTATION/SPECIFICATION.- 17 The Elements of Formal Language Theory.- A A Chapter-Long Text on Discrete Mathematics.- B SelectedExercises, by Chapter.- List of ACRONYMS and SYMBOLS.- References.- Index.