File:Schaefer's 3-SAT to 1-in-3-SAT reduction.gif

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Summary

Description
English: The left table shows the 1-in-3-SAT clauses Schaefer's reduction maps a 3-SAT clause x∨y∨z to. a,...,f are fresh variables; the result of R is true iff exactly one of its arguments is. All 8 combinations of values for x,y,z are examined, one per line. The reduction is satisfiable iff x∨y∨z is true. The right table shows a simpler reduction with the same properties.
Date
Source Own work
Author Jochen Burghardt
Other versions
Uncolored txt source 
 R(x,a,d) ∧ R(y,b,d) ∧ R(a,b,e) ∧ R(c,d,f) ∧ R(z,c,0)
 ----------------------------------------------------
 R(0,a,d) ∧ R(0,b,d) ∧ R(a,b,e) ∧ R(c,d,f) ∧ R(0,c,0)
 R(0,a,d) ∧ R(0,b,d) ∧ R(a,b,e) ∧ R(c,d,f) ∧ R(1,c,0)
 R(0,a,d) ∧ R(1,b,d) ∧ R(a,b,e) ∧ R(c,d,f) ∧ R(0,c,0)
 R(0,a,d) ∧ R(1,b,d) ∧ R(a,b,e) ∧ R(c,d,f) ∧ R(1,c,0)
 R(1,a,d) ∧ R(0,b,d) ∧ R(a,b,e) ∧ R(c,d,f) ∧ R(0,c,0)
 R(1,a,d) ∧ R(0,b,d) ∧ R(a,b,e) ∧ R(c,d,f) ∧ R(1,c,0)
 R(1,a,d) ∧ R(1,b,d) ∧ R(a,b,e) ∧ R(c,d,f) ∧ R(0,c,0)
 R(1,a,d) ∧ R(1,b,d) ∧ R(a,b,e) ∧ R(c,d,f) ∧ R(1,c,0)

 R(¬x,a,b) ∧ R(b,y,c) ∧ R(c,d,¬z)
 --------------------------------
 R( 1,a,b) ∧ R(b,0,c) ∧ R(c,d, 1)
 R( 1,a,b) ∧ R(b,0,c) ∧ R(c,d, 0)
 R( 1,a,b) ∧ R(b,1,c) ∧ R(c,d, 1)
 R( 1,a,b) ∧ R(b,1,c) ∧ R(c,d, 0)
 R( 0,a,b) ∧ R(b,0,c) ∧ R(c,d, 1)
 R( 0,a,b) ∧ R(b,0,c) ∧ R(c,d, 0)
 R( 0,a,b) ∧ R(b,1,c) ∧ R(c,d, 1)
 R( 0,a,b) ∧ R(b,1,c) ∧ R(c,d, 0)

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inception

20 September 2013

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current04:01, 21 September 2013Thumbnail for version as of 04:01, 21 September 20131,159 × 279 (19 KB)wikimediacommons>Jochen Burghardtversion in landscape layout
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