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

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.