Understanding Computation

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?

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.