Comparison of Single MDD and Series of MDDs in the Representation of Structure Function of Series-Parallel MSS

Abstract

Series-parallel topology is one of the commonly encountered system topologies of Multi-State Systems (MSSs). We use the structure function which has a form of a Multiple-Valued logic (MVL) function to describe the system. The structure function of complex MSS can be considerably large. Therefore, we use Multi-valued Decision Diagram (MDD) for its representation. A straightforward way to represent the structure function is to use a single MDD. There exists an alternative approach that uses a series of MDDs to represent the structure function. Our present research suggests that the series approach is more efficient in terms of the number of nodes in the MDD when we consider series-parallel systems. The paper deals with a further experimental comparison of the two approaches by examining random initial variable ordering dynamically adjusted using the variable sifting heuristic. Results of the new experiment confirm that given an arbitrary series-parallel topology and arbitrary ordering of variables the approach that uses a series of diagrams is more efficient and never worse considering the number of nodes in the MDD. Furthermore, the new results also show that static ordering of variables by their indices is considerably better than any dynamic ordering in the case of series-parallel systems defined using the process introduced in our previous work.