GATE | GATE CS 1999 | Question 58

[5 Marks question]

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.

Answer:
Explanation:
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