
Logic Synthesis. CNF Satisfiability. CNF Formula’s. Product of Sum (POS) representation of Boolean function Describes solution using a set of constraints very handy in many applications because new constraints can just be added to the list of existing constraints very common in AI community
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CNF Satisfiability
( a+^b+ c)
(^a+ b+ c)
( a+^b+^c)
( a+ b+ c)
Å
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
1
(a + b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a + b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + c)
(a+ b + c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
2
(a + b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a + b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + c)
(a + b + ¬c)
(a+ b + c)
(a+ b + ¬c)
(a+ b + c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
3
(¬a + b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a + b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(a+ b + ¬c)
(¬a + b + ¬c)
(a+ b + ¬c)
(¬a+ b + ¬c)
(a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(¬a+ b + ¬c)
(¬a + b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
4
(a + c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a + c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(a + c + d)
(a+ c + d)
(¬a+ b + ¬c)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(a+ c + d)
(a+ c + d)
(a + c + d)
(a + c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
5
(¬a + c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a + c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a + c + d)
(a+ c + d)
(a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a + c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(a+ c + d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a + c + d)
(¬a + c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
6
(¬a + c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a + c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + d)
(¬a+ c + d)
(¬a + c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a + c + ¬d)
(¬a+ c + ¬d)
(¬a + c + ¬d)
(¬a+ c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬a + c + ¬d)
(¬a + c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
7
(¬b + ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b + ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b + ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b + ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬a+ c + ¬d)
(¬b + ¬c + ¬d)
(¬a+ c + ¬d)
(¬b+ ¬c + ¬d)
(¬a+ c + ¬d)
(¬b + ¬c + ¬d)
(¬b + ¬c + ¬d)
(¬b + ¬c + ¬d)
(¬b + ¬c + ¬d)
(¬b + ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b + ¬c + ¬d)
(¬b + ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b + ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
8
(¬b + ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b + ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b + ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b + ¬c + d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b + ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + ¬d)
(¬b + ¬c + d)
(¬b + ¬c + d)
(¬b + ¬c + d)
(¬b + ¬c + d)
(¬b + ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b + ¬c + d)
(¬b + ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b + ¬c + d)
(¬b+ ¬c + d)
(¬b + ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
Basic Case Splitting Algorithma
b
b
c
c
c
d
d
d
d
d
Source: Karem A. Sakallah, Univ. of Michigan
1
x
1
x
x
1
0
0
1
x
x
0
x
0
0
0
0
x
x
0
0
1
0
1
1
x
a
c
b
Implications in CNFExample: (a+^b+c) (a=0)(b=1)Þ(c=1)
(^a+^b+c)(a+^c)(b+^c)
(a + b + c)
(a + b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
2
(a + b + ¬c)
(a + b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
3
(¬a + b + ¬c)
(¬a + b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
4
(a + c + d)
(a + c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
5
(¬a + c + d)
(¬a + c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
6
(¬a + c + ¬d)
(¬a + c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
7
(¬b + ¬c + ¬d)
(¬b + ¬c + ¬d)
(¬b + ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
6
(¬b + ¬c + ¬d)
(¬b + ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
8
6
5
8
4
5
7
3
(¬b + ¬c + d)
(¬b + ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b + ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
a
b
a
a
(¬b + ¬c + d)
(¬b + ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
8
6
6
5
d
d
d
c
d
7
3
5
4
b
c
c
c
8
6
6
Case Splitting with Implicationsa
b
b
c
c
Source: Karem A. Sakallah, Univ. of Michigan
9
9
9
9
9
9
9
9
9
9
9
9
9
9
(a + b + c)
(a + b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(¬b+ ¬c)
(¬b+ ¬c)
(¬b+ ¬c)
(¬b+ ¬c)
(¬b+ ¬c)
(¬b+ ¬c)
(¬b+ ¬c)
(¬b + ¬c)
(¬b+ ¬c)
(¬b+ ¬c)
(¬b+ ¬c)
(¬b + ¬c)
(¬b+ ¬c)
(¬b+ ¬c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
(a+ b + c)
2
10
10
10
10
10
10
10
10
10
10
(a + b + ¬c)
(a + b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(¬a+ ¬b)
(¬a+ ¬b)
(¬a+ ¬b)
(¬a+ ¬b)
(¬a+ ¬b)
(¬a+ ¬b)
(¬a + ¬b)
(¬a+ ¬b)
(¬a+ ¬b)
(¬a+ ¬b)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
(a+ b + ¬c)
3
11
11
11
11
11
11
(¬a + b + ¬c)
(¬a + b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a)
(¬a)
(¬a)
(¬a)
(¬a)
(¬a)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
(¬a+ b + ¬c)
4
(a + c + d)
(a + c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
(a+ c + d)
6
(a+ c + d)
(a+ c + d)
6
4
11
5
5
5
a
(¬a + c + d)
(¬a + c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
a
a
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
(¬a+ c + d)
3
6
9
6
(¬a + c + ¬d)
(¬a + c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
(¬a+ c + ¬d)
c
b
5
(¬a+ c + ¬d)
(¬a+ c + ¬d)
d
(¬a+ c + ¬d)
(¬a+ c + ¬d)
6
9
4
3
5
10
b
c
d
d
c
b
6
7
(¬b + ¬c + ¬d)
(¬b + ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b + ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b + ¬c + ¬d)
(¬b + ¬c + ¬d)
(¬b+ ¬c + ¬d)
(¬b+ ¬c + ¬d)
6
8
8
7
(¬b + ¬c + d)
(¬b + ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
(¬b + ¬c + d)
b
(¬b + ¬c + d)
(¬b + ¬c + d)
(¬b+ ¬c + d)
(¬b+ ¬c + d)
9
10
8
(¬b + ¬c)
(¬a+ ¬b)
d
7
c
8
Conflict-based Learninga
a® ¬j
ß
j ® (¬a)
ab® ¬j
ß
j ® (¬a + ¬b)
bc® ¬j
ß
j ® (¬b + ¬c)
b
b
c
Source: Karem A. Sakallah, Univ. of Michigan