University of Central Florida
School of Computer Science
COT 4210
Spring 2004
Prof. Rene Peralta
Homework 7
Due date: April 19
1. The following is a hierarchy of subsets of
IN
.
regular
CFL
recursive
re.
P
(
IN
)
Show that the hierarchy is proper by giving examples of sets contained
in each level but not in the next one.
2. In this question, let
M
be a Turing machine which takes as input
a positive integer
i
and outputs (if it halts) a positive integer
M
(
i
).
Denote by
L
M
the language
{
M
(
i
)

i
= 1
,
2
,
3
, . . .
}
.
Answer True or False (no need to justify your answer, do so at your
own peril). Score is +1 for correct answer, 1 for incorrect answer.
(a) It is always true that the language
L
M
is recursive.
(b) The set of languages over
{
0
,
1
}
recognized by C programs is
countable.
(c) There exists a language recognized by
M
but not recognized by
any Finite Automaton.
(d) Let
H
be the language composed of Turing machine represen
tations which halt iff the input is an even number.
Then
H
is
computable in polynomial time.
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 Spring '08
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 Computer Science, Halting problem, Recursively enumerable language

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