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Handout #51
CS103
November 17, 2010
Robert Plummer
Problem Set #9—Due
Friday
, December 3 in class
No late days may be used for this assignment
1.
Suppose that B is a decidable language, that w
1
B, and that w
2
B.
Prove that a
language A is decidable if and only if A
m
B.
The parts of your proof will thus be:
(a)
Prove that if A
m
B, then A is decidable.
(b)
Prove that if A is decidable, then A
m
B.
In this part of the proof, you need to
specify a mapping.
Do this in the style of Example 5.24; that is, specify a Turing
machine that does the mapping, in Sipser's style: "F = "On input .
..".
Then you must
argue why your mapping is correct; that is, why it meets the requirements necessary for
mapping reductions.
2.
We have seen that some languages are neither Turing recognizable nor coTuring
recognizable.
In this problem, we consider another such language, defined as follows:
L = { w  either w = 0x for some x
A
TM
, or w = 1y for some y
A
TM
}
Show that neither L nor L is Turing recognizable.
3. Prove or disprove: there exists an undecidable language A such that A
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This document was uploaded on 02/08/2011.
 Fall '09

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