Linear Decision Diagrams∗

We introduce linear decision diagrams (LDDs) as a special class of linear representations of formal power series. LDDs can be seen as a generalization of some previously proposed structures, such as MTBDDs and matrix diagrams, that have seen successful application in the compact representation of Markov models with large state spaces. Besides providing some possibilities for additional compression, LDDs have an interesting and useful reversibility property that is not shared by previously considered BDD variants. In addition, LDDs have the advantage that most LDD operations can be performed without any assumption that the arguments are fully reduced or “canonical.” This suggests the possibility of using multiple reduction heuristics that trade off reduction “strength” for computation cost. We present some experimental results that compare the sizes of MTBDD and LDD representations for rate matrices obtained from some standard benchmark examples.