Prove:Church’s thesis: The class of computable functions is equal to the class of intuitive computable functions.
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Prove:Church’s thesis: The class of computable functions is equal to the class of intuitive computable functions.
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- 1. For the function defined recursively by f(0)=5 and f(n)=4f (n-1)+3, answer the following: a. Find a closed form representation for this function. Your closed form should not include any series. b. Prove that your representation is correct using a formal inductive argument.2- consulting D, Character, verify that: a) The characters of classes C, and C, are for all irreducible representations are orthogonal. b) The characters of the irreducible representation B, for all classes are normalized.Reduce the following lambda-calculus terms to the normal form. Show all intermediate steps, with one beta reduction at a time. In the reduction, if necessary, assume that you are supplied with extra rules that allow you to reduce the addition of two natural numbers into the corresponding result. (λz. z) (λy. y y) (λx. x a)
- Discrete mathematics applied to computer science: homework question. Let f : A → A be a function in the domain A =/= ∅. Confirm or deny, with justification: f is a bijection if and only if the composition f ◦ f is a bijection. I don't understand how I should approach this problem. Thank you for your gracious help.Computer Science In function f(x) ->y the domain of x is continuous in the range 1-10how many equivalence classes are there in this case?Write a highly efficient MATLAB code to execute the following steps. Your code should NOT include the following MATLAB functions or keywords: if, for, while. In other words, you will lose all points for this quiz if any of if, for, while appears in your code.
- Answer the following multiple choice questions: - If B represented the set of Boolean values true and false, then the set of Boolean functions B x B → B is... A) finite B) uncountably infinite C) countably infinite - The set of functions from {0,1} to N is... A) finite B) uncountably infinite C) countably infinite - The set of functions from N to {0,1} is... A) finite B) uncountably infinite C) countably infiniteProve the axiomatic program as described below:Which functions are one-to-one? Which functions are onto? Describe the inversefunction for any bijective function.(a) f : Z → N where f is defined by f (x) = x4 + 1(b) f : N → N where f is defined by f (x) = { x/2 if x is even, x + 1 if x is odd}(c) f : N → N where f is defined by f (x) = { x + 1 if x is even, x − 1 if x is odd}
- How does the Structured Programming Theorem shed light on the GOTO mess and convoluted code? Please do so in your own words and in an essay of an appropriate length for the assignment.Design a class for solving quadratic equation that apply loose coupling and high cohesion.2. Consider a function with polymorphic type f : 'а -> 'a -> 'a. 2.1. What is the type of f 0 ? 2.2. What is the type of fun x -> f x x ? Briefly explain your reasoning.