Implication Graph

computation

Definition

Implication Graph

$$\begin{array}{rl}F=& (\neg x_2⟹x_0)\wedge (\neg x_0⟹x_2)\wedge (x_3⟹x_0)\wedge (\neg x_0⟹\neg x_3)\\ & \wedge (x_3⟹x_1)\wedge (\neg x_1⟹\neg x_3)\wedge (x_4⟹x_1)\wedge (\neg x_1⟹\neg x_4)\\ & \wedge (x_4⟹x_2)\wedge (\neg x_2⟹\neg x_4)\wedge (\neg x_4⟹x_6)\wedge (\neg x_6⟹x_4)\\ & \wedge (\neg x_5⟹x_6)\wedge (\neg x_6⟹x_5)\wedge (x_5⟹x_0)\wedge (x_5⟹x_1)\\ & \wedge (x_5⟹x_2)\wedge (\neg x_2⟹\neg x_5)\wedge (\neg x_1⟹\neg x_5)\wedge (\neg x_0⟹\neg x_5)\\ & \wedge (\neg x_3⟹x_6)\wedge (\neg x_6⟹x_3).\end{array}$$

Its implication graph is given by: