4.B: Computable functions and mapping reduction
Course week(s)
Week 4
Course subject(s)
4: Reducibility
Description: Turing machines can also be used to compute functions: given an input x, compute f(x). Functions that can be computed that way are called computable functions. Mapping reduction is defined by means of the notion of computable function. Some examples are given using mapping reduction to prove that certain sets are not decidable or not recognisable.
Book: Introduction to the Theory of Computation, Chapter 5, pp. 210-214.
Exercises: 5.4-5.7, 5.20, 5.22, 5.23 and 5.25.
Key concepts:
- Direct Reduction
- Mapping Reduction
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