Theoretical Computer Science for the Working Category Theorist

Description

Using basic category theory, this Element describes all the central concepts and proves the main theorems of theoretical computer science. Category theory, which works with functions, processes, and structures, is uniquely qualified to present the fundamental results of theoretical computer science. In this Element, readers will meet some of the deepest ideas and theorems of modern computers and mathematics, such as Turing machines, unsolvable problems, the P=NP question, Kurt Gödel's incompleteness theorem, intractable problems, cryptographic protocols, Alan Turing's Halting problem, and much more. The concepts come alive with many examples and exercises. Cover Title Page Copyright Page Theoretical Computer Science for the Working Category Theorist Contents Preface 1 Introduction 2 Aide-Mémoire on Category Theory 2.1 Slice Categories and Comma Categories 3 Models of Computation 3.1 The Big Picture 3.2 Manipulating Strings 3.3 Manipulating Natural Numbers 3.4 Manipulating Bits 3.5 Logic and Computation 3.6 Numbering Machines and Computable Functions 4 Computability Theory 4.1 Turing’s Halting Problem 4.2 Other Unsolvable Problems 4.3 Classifying Unsolvable Problems 5 Complexity Theory 5.1 Measuring Complexity 5.2 Decision Problems 5.3 Space Complexity 6 Diagonal Arguments 6.1 Cantor’s Theorem 6.2 Applications in Computability Theory 6.3 Applications in Complexity Theory 7 Conclusion 7.1 Looking Back 7.2 Moving Forward References Acknowledgements Index