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Great Ideas in Theoretical Computer Science: Computability

Ryan O'Donnell via YouTube

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This lecture introduces Turing machines as a formal model of computation, covering decidable languages, universal machines, the Church–Turing thesis, and undecidable problems including the Halting Problem.

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

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