22C:131 Limits of Computation

Lecture Notes for Fall Semester 2009

Class Management

Part 1: Mathematical Background

Part 2: Finite Automata and Regular Languages

Part 3: Context-Free Grammars and Pushdown Automata

Part 4: Truring Machines and the Concept of an Algorithm

  • Turing Machines
  • Examples of Turing Machines
  • Variants of Turing Machines
  • The Definition of Algorithm
  • Algorithms and recursive functions
  • Hyper-computation: Why interaction is more powerful than algorithms? (P.Wegner, Comm. ACM, 1997)

    • Part 5: Decidability Theory

  • Decidability: Decidable Problems Concerning Regular Languages
  • Decidable Problems Concerning CFL
  • Halting Problem and Diagonalization Method
  • Reducibility: A Methodology for Proving Unsolvability
  • Reduction via Computation Histories
  • Post Correspondence Problem
  • Mapping Reducibility