Explain minimization applied to exponentiation

Reference no: EM131912008

Basics of Computability Theory

Exercise 1 Give one concrete example for each of the Basic Functions (The zero, successor, identity or projection functions).

Exercise 2 Define Composition (f o g)(x) for functions f (x) = x × 2 and g(x) = x³ - 2.

Exercise 3 Give concrete examples of all primitive recursions schema for arithmetical functions on inputs m, n of your choice.

Exercise 4 Consider the Exponentiation function x^y. Explain Minimization applied to Exponentiation: is it regular? i.e. is there for every input x to exponentiation a value of y such that x^y = 0? Is it undefined?

Exercise 5 Give an example of a partial arithmetical function.

Reference no: EM131912008

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