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Table 7 16 possible PC logic functions between two genes G1 and G2, which regulate the target. The ∪ sign stands for the union of the sets, and ∨, ∧ , ⊕ , and ⨀ stand for the OR, AND, XOR, and XNOR PC logics between G1 and G2

From: LogicNet: probabilistic continuous logics in reconstructing gene regulatory networks

i

i3

i2

i1

i0

fi(G1, G2)

Output

0

0

0

0

0

0

0

1

0

0

0

1

\( \overline{G_1}\overline{G_2}=\overline{G_1}\wedge \overline{G_2} \)

\( \left(1-{\mathit{\exp}}_{G_1}\right)\ast \left(1-{\mathit{\exp}}_{G_2}\right) \)

2

0

0

1

0

\( \overline{G_1}{G}_2=\overline{G_1}\wedge {G}_2 \)

\( {\mathit{\exp}}_{G_2}-{\mathit{\exp}}_{G_1}\ast {\mathit{\exp}}_{G_2} \)

3

0

0

1

1

\( \overline{G_1}{G}_2\cup \overline{G_1}\overline{G_2}=\overline{G_1} \)

\( 1-{\mathit{\exp}}_{G_1} \)

4

0

1

0

0

\( {G}_1\overline{G_2}={G}_1\wedge \overline{G_2} \)

\( {\mathit{\exp}}_{G_1}-{\mathit{\exp}}_{G_1}\ast {\mathit{\exp}}_{G_2} \)

5

0

1

0

1

\( {G}_1\overline{G_2}\cup \overline{G_1}\overline{G_2}=\overline{G_2} \)

\( 1-{\mathit{\exp}}_{G_2} \)

6

0

1

1

0

\( {G}_1\overline{G_2}\cup \overline{G_1}{G}_2={G}_1\bigoplus {G}_2 \)

\( {\mathit{\exp}}_{G_1}+{\mathit{\exp}}_{G_2}-2\ {\mathit{\exp}}_{G_1}\ast {\mathit{\exp}}_{G_2} \)

7

0

1

1

1

\( {G}_1\overline{G_2}\cup \overline{G_1}{G}_2\cup \overline{G_1}\overline{G_2}=\overline{G_1}\vee \overline{G_2} \)

\( 1-{\mathit{\exp}}_{G_1}\ast {\mathit{\exp}}_{G_2} \)

8

1

0

0

0

G1G2 = G1 ∧ G2

\( {\mathit{\exp}}_{G_1}\ast {\mathit{\exp}}_{G_2} \)

9

1

0

0

1

\( {G}_1{G}_2\cup \overline{G_1}\overline{G_2}={G}_1\bigodot {G}_2 \)

\( 1-{\mathit{\exp}}_{G_1}-{\mathit{\exp}}_{G_2}+2\ {\mathit{\exp}}_{G_1}\ast {\mathit{\exp}}_B \)

10

1

0

1

0

\( {G}_1{G}_2\cup \overline{G_1}{G}_2={G}_2 \)

\( {\mathit{\exp}}_{G_2} \)

11

1

0

1

1

\( {G}_1{G}_2\cup \overline{G_1}{G}_2\cup \overline{G_1}\overline{G_2}=\overline{G_1}\vee {G}_2 \)

\( 1-{\mathit{\exp}}_{G_1}+{\mathit{\exp}}_{G_1}\ast {\mathit{\exp}}_{G_2} \)

12

1

1

0

0

\( {G}_1{G}_2\cup {G}_1\overline{G_2}={G}_1 \)

\( {\mathit{\exp}}_{G_1} \)

13

1

1

0

1

\( {G}_1{G}_2\cup {G}_1\overline{G_2}\cup \overline{G_1}\overline{G_2}={G}_1\vee \overline{G_2} \)

\( 1-{\mathit{\exp}}_{G_2}+{\mathit{\exp}}_{G_1}\ast {\mathit{\exp}}_{G_2} \)

14

1

1

1

0

\( {G}_1{G}_2\cup {G}_1\overline{G_2}\cup \overline{G_1}{G}_2={G}_1\vee {G}_2 \)

\( {\mathit{\exp}}_{G_1}+{\mathit{\exp}}_{G_2}-{\mathit{\exp}}_{G_1}\ast {\mathit{\exp}}_{G_2} \)

15

1

1

1

1

\( {G}_1{G}_2\cup {G}_1\overline{G_2}\cup \overline{G_1}{G}_2\cup \overline{G_1}\overline{G_2}=1 \)

1