Explore the foundations of computability theory in this lecture from CMU's "Great Ideas in Theoretical Computer Science" course. Delve into Turing Machines, their formal definition, and programming exercises. Examine the concept of decidable languages and the Church-Turing Thesis. Investigate uncomputable functions and the undecidability of the Halting Problem. Learn about the historical context of computation and algorithms, including Turing's inspiration from early computers.
Great Ideas in Theoretical Computer Science: Computability
Overview
Syllabus
15-251: Great Theoretical ideas in Computer Science Lecture 22
What is a computation/algorithm?
Turing's inspiration: computers (usage 2)
The finite control (AKA transition rules)
Formal definition of Turing Machines
Decidable languages
TM programming exercises & tricks
Universal Turing Machine
TM's: good definition of computation?
Church-Turing Thesis: "Any natural / reasonable notion of computation can be simulated by a TM."
Describing Turing Machines
Some uncomputable functions
Does the following program (written in Maple) print out "HELLO WORLD" ?
The Halting Problem is Undecidable
Taught by
Ryan O'Donnell
