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

) represent the constant Boolean function which always evaluates to 1 (0).

A leaf labeled with a Boolean variable

-node represents the complementary 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.

Every binary decision diagram (BDD) and every negation normal form (NNF) are also a PDAG with some particular properties.

The following pictures represent the Boolean function