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1800
1600
number errors corrected
1400
1200
1000
800
600
400
200
0
0.2
0.25
0.3
0.35
rate
0.4
0.45
0.5
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probability decoded
0.7
0.6
0.5
0.4
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1750
1800
1850
1900
number of errors
1950
2000
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Theorem:
C’ is satisfiable.
Holographic proof that
C’ is satisfied by
E(p(x)) and E(v)
check proof
Proof-checker
E(v)
check that satisfying assignment in proof
actually is this assignment.
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8
4x
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2
3
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2
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Proof:
(7x-1)(0,1,2) = (-1,6,13)
E(-1) E(6)
E(13) E(7x-1)
Proof:
(4x)(0,1,2) = (0,4,8)
E(0)
E(4)
E(8)
E(4x)
Proof:
(x+1)(0,1,2) = (1,2,3)
E(1)
E(2)
E(3)
E(x+1)
one check
Checker provides:
m
X@i
p
Theorem (encoded):
p(x)(0,1,2) = (a,b,c)
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