CS 2250

Author

Affiliation

Clayton Cafiero

University of Vermont

Computability and Complexity

Textbook: Sipser, Michael. 2013. Introduction to the Theory of Computation, 3rd ed. Cengage

Topics:

• Introduction to TOC; mathematical foundations and proof techniques
• Regular languages; finite automata; regular expressions; non-regular languages
• Context-free languages; context-free grammars; pushdown automata
• Church-Turing thesis; Turing machines and variants; algorithms
• Decidability; diagonalization; undecidable languages
• Reducibility; computable functions; mapping reducibility
• Complexity theory: P, NP, NP-complete, NP hard

Selected materials

Introduction

• What are automata?
• What is computability?
• What is complexity?
• Some matters of notation
• Functions as sets
• Set union

Regular languages

• Formal definitions
• State diagrams
• DFAs and NFAs

Context-free languages

• Material forthcoming

The Church-Turing thesis

• Material forthcoming

Decidability

• Material forthcoming

Reducibility

• Material forthcoming

Time complexity

• Material forthcoming

Miscellaneous

• Some handy tips for proofs involving Turing machines