Question

The Ackerman function is given as follows. (A(0,n)=n+1
A(m,0)=A(m-1,1) If m>0
A(m,n)=A(m-1,A(m,m-1)) if m>0 and n>0
Calculate A(0,2) and A(2,0).

Answer 1

Given Ackermann function:

• $A(0,n)=n+1$

• $A(m,0)=A(m-1,1)$ if $m>0$

• $A(m,n)=A(m-1,A(m,m-1))$ if $m,n>0$

To find: $A(0,2)$ and $A(2,0)$

Step-by-step explanation:

Now, $A(0,2)=2+1=3$ [ using the 1st condition ]

and $A(2,0)$

$=A(2-1,1)$ [ using the 2nd condition ]

$=A(1,1)$

$=A(1-1,A(1,1-1))$ [ using the 3rd condition ]

$=A(0,A(1,0))$

$=A(0,A(1-1,1))$ [ using the 2nd condition ]

$=A(0,A(0,1))$

$=A(0,1+1)$ [ using the 1st condition ]

$=A(0,2)$

$=3$ [ calculated previously ]

Answer: $A(0,2)=A(2,0)=3$