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Home Courses Theory of Computation Course materials Lectures 4.B: Computable functions and mapping reduction

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.

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Key concepts:

Direct Reduction
Mapping Reduction

Module 4B

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