Multiway Decision Diagrams Research Articles

Approximate steady-state analysis of large Markov models based on the structure of their decision diagram encoding

We propose a new approximate numerical algorithm for the steady-state solution of general structured ergodic Markov models. The approximation uses a state–space encoding based on multiway decision diagrams and a transition rate encoding based on a new class of edge-valued decision diagrams. The new method retains the favorable properties of a previously proposed Kronecker-based approximation, while eliminating the need for a Kronecker-consistent model decomposition. Removing this restriction allows for a greater utilization of event locality, which facilitates the generation of both the state–space and the transition rate matrix, thus extends the applicability of this algorithm to larger and more complex models.

Saturation for a General Class of Models

Implicit techniques for construction and representation of the reachability set of a high-level model have become quite efficient for certain types of models. In particular, previous work developed a "saturation" algorithm that exploits asynchronous behavior to efficiently construct the reachability set using multiway decision diagrams, but using a Kronecker product expression to represent each model event. For models whose events do not naturally fall into this category, use of the saturation algorithm requires adjusting the model by combining components or splitting events into subevents until a Kronecker product expression is possible. In practice, this can lead to additional overheads during reachability set construction. This paper presents a new version of the saturation algorithm that works for a general class of models: models whose events are not necessarily expressible as Kronecker products, models containing events with complex priority structures, and models whose state variables have unknown bounds. Experimental results are given for several examples

The saturation algorithm for symbolic state-space exploration

We present various algorithms for generating the state space of an asynchronous system based on the use of multiway decision diagrams to encode sets and Kronecker operators on boolean matrices to encode the next-state function. The Kronecker encoding allows us to recognize and exploit the “locality of effect” that events might have on state variables. In turn, locality information suggests better iteration strategies aimed at minimizing peak memory consumption. In particular, we focus on the saturation strategy, which is completely different from traditional breadth-first symbolic approaches, and extend its applicability to models where the possible values of the state variables are not known a priori. The resulting algorithm merges “on-the-fly” explicit state-space generation of each submodel with symbolic state-space generation of the overall model.Each algorithm we present is implemented in our tool SmArT. This allows us to run fair and detailed comparisons between them on a suite of representative models. Saturation, in particular, is shown to be many orders of magnitude more efficient in terms of memory and time with respect to traditional methods.