Can matrix-layout-independent numerical solvers be efficient?: implementing the Moebius state-level abstract functional interface for ZDDs

Abstract

Symbolic approaches based on decision diagrams have shown to be well suited for representing very large continuous-time Markov chains (CTMC), as derived from high-level model descriptions. Unfortunately, each type of decision diagram requires its own implementation of the numerical solvers for computing the state probabilities of the CTMC. For this reason, some time ago the idea of separating numerical solution methods from the representation of the CTMC was proposed [12], suggesting the implementation of a so-called state-level abstract functional interface (AFI), which defines classes of iterators for accessing the entries of the CTMC transition rate matrix. In this paper we (a) present an implementation of the AFI for zero-suppressed multi-terminal binary decision diagrams (ZDDs) [18] and (b) empirically investigate the viability of matrix-layout-independent implementations of numerical solvers.