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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 = G1G2 \( {\mathit{\exp}}_{G_1}\ast {\mathit{\exp}}_{G_2} \)
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