Alapfogalmak
This document provides a unified introduction to binary decision diagrams and Boolean circuits, highlighting the connections between these formalisms and automata on words and trees.
Kivonat
The document starts by introducing the basic definitions and properties of nondeterministic binary decision diagrams (nBDDs), including notions of variable structuredness (free, ordered) and ambiguity levels (nondeterministic, unambiguous, deterministic). It then presents the formalism of Boolean circuits, defining similar concepts of variable structuredness (decomposable, structured) and ambiguity levels.
The key insights are:
Binary decision diagrams can be seen as a special case of Boolean circuits, and there are polynomial-time translations between the two formalisms.
There are deep connections between conditions on automata (determinism, unambiguity) and conditions on the corresponding binary decision diagrams or Boolean circuits.
The document introduces the notion of provenance circuits, which relate automata to Boolean functions describing their behavior. This provides a "Rosetta stone" for translating between the different formalisms.
The document also discusses completeness for binary decision diagrams and smoothness for Boolean circuits, as well as alternative semantics like zero-suppressed semantics.
Overall, the document aims to serve as a unifying introduction to these related formalisms, encouraging further interaction between the communities studying them.