October 22, 2023
October 22, 2023
October 22, 2023
###### Computer-Networks
October 22, 2023
 Question 1

Suppose we have a function HALTS which when applied to any arbitrary function f and its arguments will say TRUE if function f terminates for those arguments and FALSE otherwise. Example, Given the following function definition.
FACTORIAL (N) = IF(N=0) THEN 1 ELSE N*FACTORIAL (N-1)
Then HALTS(FACTORIAL 4) = TRUE and HATS(FACTORIAL – 5) = FALSE

Let us define the function FUNNY(f) = IF HALTS(ff) THEN not(ff) ELSE TRUE
(a) Show that FUNNY terminates for all functions f.
(b) Use (a) to prove (by contradiction) that it is not possible to have a function like HALTS which for arbitrary functions and inputs says whether it will terminate on that input or not.

 A Theory Explanation.
Correct Answer: A
##### R Rama
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