Reduction of satisfiability to integer linear programming
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Given an instance of SAT, how do I exhibit that instance of SAT into ILP? Do I have to find the satisfying assignment for f first or does this not matter?
computational-complexity
asked Nov 18 at 14:03
C.Lako
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Given an instance of SAT, how do I exhibit that instance of SAT into ILP? Do I have to find the satisfying assignment for f first or does this not matter?
computational-complexity
asked Nov 18 at 14:03
C.Lako
263
You're going to produce an ILP whose solution (if it exists) can be transformed back into a solution of the original SAT problem. You don't need to find a satisfying assignment first (and one might not exist.)
– Brian Borchers
Nov 18 at 15:43
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Given an instance of SAT, how do I exhibit that instance of SAT into ILP? Do I have to find the satisfying assignment for f first or does this not matter?
computational-complexity
asked Nov 18 at 14:03
C.Lako
263
Given an instance of SAT, how do I exhibit that instance of SAT into ILP? Do I have to find the satisfying assignment for f first or does this not matter?
computational-complexity
computational-complexity
asked Nov 18 at 14:03
C.Lako
263
asked Nov 18 at 14:03
C.Lako
263
asked Nov 18 at 14:03
C.Lako
263
asked Nov 18 at 14:03
C.Lako
263
asked Nov 18 at 14:03
C.Lako
263
263
You're going to produce an ILP whose solution (if it exists) can be transformed back into a solution of the original SAT problem. You don't need to find a satisfying assignment first (and one might not exist.)
– Brian Borchers
Nov 18 at 15:43
add a comment |
You're going to produce an ILP whose solution (if it exists) can be transformed back into a solution of the original SAT problem. You don't need to find a satisfying assignment first (and one might not exist.)
– Brian Borchers
Nov 18 at 15:43
You're going to produce an ILP whose solution (if it exists) can be transformed back into a solution of the original SAT problem. You don't need to find a satisfying assignment first (and one might not exist.)
– Brian Borchers
Nov 18 at 15:43
You're going to produce an ILP whose solution (if it exists) can be transformed back into a solution of the original SAT problem. You don't need to find a satisfying assignment first (and one might not exist.)
– Brian Borchers
Nov 18 at 15:43
add a comment |
1 Answer
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Recall that in SAT, you are given a Boolean formula:
$F = (x_1 + x_2 + bar{x_2}) * (x_4 + x_5) + ... $
Note that $F$ is satisfiable iff every clause is satisfiable.
That is, for each clause, at least one of the $x_i$ is true.
If we represent true by 1 and false by 0, we can reduce SAT to ILP by creating a constraint for each clause:
$x_1 + + x_2 + bar{x_2} ge 1$
$x_4 + + x_5 ge 1$
...
answered Nov 25 at 0:02
user137481
1,7752921
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
Recall that in SAT, you are given a Boolean formula:
$F = (x_1 + x_2 + bar{x_2}) * (x_4 + x_5) + ... $
Note that $F$ is satisfiable iff every clause is satisfiable.
That is, for each clause, at least one of the $x_i$ is true.
If we represent true by 1 and false by 0, we can reduce SAT to ILP by creating a constraint for each clause:
$x_1 + + x_2 + bar{x_2} ge 1$
$x_4 + + x_5 ge 1$
...
answered Nov 25 at 0:02
user137481
1,7752921
add a comment |
up vote
0
down vote
Recall that in SAT, you are given a Boolean formula:
$F = (x_1 + x_2 + bar{x_2}) * (x_4 + x_5) + ... $
Note that $F$ is satisfiable iff every clause is satisfiable.
That is, for each clause, at least one of the $x_i$ is true.
If we represent true by 1 and false by 0, we can reduce SAT to ILP by creating a constraint for each clause:
$x_1 + + x_2 + bar{x_2} ge 1$
$x_4 + + x_5 ge 1$
...
answered Nov 25 at 0:02
user137481
1,7752921
add a comment |
up vote
0
down vote
up vote
0
down vote
Recall that in SAT, you are given a Boolean formula:
$F = (x_1 + x_2 + bar{x_2}) * (x_4 + x_5) + ... $
Note that $F$ is satisfiable iff every clause is satisfiable.
That is, for each clause, at least one of the $x_i$ is true.
If we represent true by 1 and false by 0, we can reduce SAT to ILP by creating a constraint for each clause:
$x_1 + + x_2 + bar{x_2} ge 1$
$x_4 + + x_5 ge 1$
...
answered Nov 25 at 0:02
user137481
1,7752921
Recall that in SAT, you are given a Boolean formula:
$F = (x_1 + x_2 + bar{x_2}) * (x_4 + x_5) + ... $
Note that $F$ is satisfiable iff every clause is satisfiable.
That is, for each clause, at least one of the $x_i$ is true.
If we represent true by 1 and false by 0, we can reduce SAT to ILP by creating a constraint for each clause:
$x_1 + + x_2 + bar{x_2} ge 1$
$x_4 + + x_5 ge 1$
...
answered Nov 25 at 0:02
user137481
1,7752921
answered Nov 25 at 0:02
user137481
1,7752921
answered Nov 25 at 0:02
user137481
1,7752921
answered Nov 25 at 0:02
user137481
1,7752921
1,7752921
add a comment |
add a comment |
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You're going to produce an ILP whose solution (if it exists) can be transformed back into a solution of the original SAT problem. You don't need to find a satisfying assignment first (and one might not exist.)
– Brian Borchers
Nov 18 at 15:43