CS 15-212: Fundamental Structures of Computer Science II

In this lecture we discuss the central results about the computability of functions in ML. By the Church-Turing thesis this is the same notion of computability as we have in recursion theory, with Turing machines, etc. There are two main ideas to show that certain functions are not computable: diagonalization (which is a direct argument), and problem reduction (which shows that a problem is undecidable by given a reduction from an another undecidable problem).

Key Concepts

• Decision problem
• Ill-posed problem
• Halting problem
• Decision procedure
• Semi-decision procedure
• Diagonalization argument
• Problem reduction
• Equality of functions

Sample Code

Handouts

• Basic Computability Theory (also in PDF format)