Lecture 19

• The relationship between the theory of Turing Machines and practice
• The notion of reduction and its applications

Slide index

• 15-453 FLAC Lecture 19: Turing Machines and Real Life * Reductions.
• A Turing Machine solves one problem.
• First computers: custom computing machines.
• TMs can be described using text.
• There is a TM which can simulate any other TM (Alan Turing, 1930).
• The Digital Computer: a UTM.
• Random Access Memories.
• Turing machines as functions.
• Computable functions.
• Compilers: computable functions.
• Multiple levels of virtualization.
• The operating system: another (multi-tape) universal Turing machine.
• The operating system = dovetailing.
• Reconfigurable hardware.
• Reconfigurable hardware (2).
• Reductions between languages.
• Reductions are useful.
• Using reductions to prove undecidability.
• Undecidability.
• Some undecidable problems.
• Compilers and undecidability.
• The full-employment theorem for compiler-writers.
• Research in programming languages.
• Reduction examples.
• A reduction from ~HP to FIN.
• Reducing ~HP to FIN (end).
• Part 2: Reducing ~HP to ~FIN.
• Reducing ~HP to ~FIN (end).
• To remember.