III Calculating Programs Suppose that you are part of a team developing an avionics software system. There is a component in the system that reads values from the physical environment, transforms those values into natural numbers and converts them using a function f defined as: f(0) =0, f(1) =1, and f(k+2) = f(k) +f(k+1) for k≥0 . According to the system requirements, there are three program variables x, y, and n that need to be updated every few seconds maintaining the following system invariant: (1) x = f(n) ∧ y = f(n+1) . It is assumed that this invariant should be valid throughout the execution of the system. The requirements also specify that the value of the program variable n is initially zero and should be incremented by 1 whenever x and y are updated. Now, answer the following questions: Question 1 (5%) What are the values of f(0), f(1), f(2) and f(3) ? Your answer should make clear how the definition of f is used.

any help is appreciated , i dont want the answer just a more in depth explanation of whats going on

thanks dale

This post has been edited by **macosxnerd101**: 07 January 2013 - 10:09 AM

Reason for edit:: Renamed title to be more descriptive