# 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

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