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COT 6410
Fall 2010
Final Exam Sample Questions
1
. Let set
A
be recursive,
B
be re nonrecursive and
C
be nonre. Choosing from among
(REC)
recursive
,
(RE)
re nonrecursive
,
(NR)
nonre
, categorize the set
D
in each of a) through d) by
listing
all
possible categories. No justification is required.
a.) D = ~C
b.) D
(A
C)
c.) D = ~B
d.) D = B
A
2.
Prove that the
Halting Problem
(the set
K
0
)
is not recursive (decidable) within any formal model of
computation. (Hint: A diagonalization proof is required here.)
3.
Using reduction from the known undecidable
HasZero, HZ = { f 
x f(x) = 0 }
, show the non
recursiveness (undecidability) of the problem to decide if an arbitrary primitive recursive function
g
has the property
IsZero, Z = { f 
x f(x) = 0 }
.
4
. Choosing from among
(D)
decidable
,
(U)
undecidable
,
(?)
unknown
, categorize each of the
following decision problems. No proofs are required.
Problem / Language Class
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 Fall '10
 Dutton

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