Propositional directed acyclic graph

A propositional directed acyclic graph (PDAG) is a data structure that is used to represent a Boolean function. A Boolean function can be represented as a rooted, directed acyclic graph of the following form:

Leaves labeled with ${\displaystyle \top }$ (${\displaystyle \bot }$) represent the constant Boolean function which always evaluates to 1 (0). A leaf labeled with a Boolean variable ${\displaystyle x}$ is interpreted as the assignment ${\displaystyle x=1}$, i.e. it represents the Boolean function which evaluates to 1 if and only if ${\displaystyle x=1}$. The Boolean function represented by a ${\displaystyle \bigtriangleup }$-node is the one that evaluates to 1, if and only if the Boolean function of all its children evaluate to 1. Similarly, a ${\displaystyle \bigtriangledown }$-node represents the Boolean function that evaluates to 1, if and only if the Boolean function of at least one child evaluates to 1. Finally, a ${\displaystyle \Diamond }$-node represents the complemenatary Boolean function its child, i.e. the one that evaluates to 1, if and only if the Boolean function of its child evaluates to 0.

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