Some notes on the abstraction operation for Multi-Terminal Binary Decision Diagrams

TL;DR

This paper clarifies the conditions under which the abstraction operation in Multi-terminal Binary Decision Diagrams (MTBDDs) is order-independent, correcting misconceptions in existing literature and extending the analysis to more general algebraic structures.

Contribution

It provides a necessary and sufficient condition for order-independence of the abstraction operation in MTBDDs within monoids and magmas, addressing inaccuracies in prior statements.

Findings

Established conditions for order-independence in MTBDDs

Extended analysis from monoids to magmas

Corrected misconceptions in existing literature

Abstract

The starting point of this work are inaccurate statements found in the literature for Multi-terminal Binary Decision Diagrams (MTBDDs) regarding the well-definedness of the MTBDD abstraction operation. The statements try to relate an operation * on a set of terminal values M to the property that the abstraction over this operation does depend on the order of the abstracted variables. This paper gives a necessary and sufficient condition for the independence of the abstraction operation of the order of the abstracted variables in the case of an underlying monoid and it treats the more general setting of a magma.