1 the post correspondence problem continued. 2 1. we will prove that the mpc problem is undecidable...
Post on 19-Dec-2015
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2
1. We will prove that the MPC problem is undecidable
2. We will prove that the PC problem is undecidable
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1. We will prove that the MPC problem is undecidable
We will reduce the membership problemto the MPC problem
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The reduction of the membership problemto the MPC problem:
For unrestricted grammar and string G w
we construct a pair such thatBA,
BA, has an MPC-solution if and only if )(GLw
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A
FS
B
FF : special symbol
aa For every symbol
Grammar G
S : start variable
a
V V For every variable V
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EcaaaCAabBAaSF
A
B
1w
aaacaACaABbS
10w
1v 10v
14w 2w 5w 12w
14v 2v 5v 12v 14v 2v 13v 9v
14w 2w 13w 9w
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Algorithm for membership problem:
Input: unrestricted grammar string
Gw
Construct the pair BA,
If has an MPC-solution then BA, )(GLw
else )(GLw
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2. We will prove that the PC problem is undecidable
We will reduce the MPC problemto the PC problem