Towards State Space Reduction Based on T-Lumpability-Consistent Relations

Abstract

Abstract. Markovian behavioral equivalences can be exploited for state space reduction before performance evaluation takes place. It is known that Markovian bisimilarity corresponds to ordinary lumpability and that Markovian testing and trace equivalences correspond to a coarser exact relation we call T-lumpability. While there exists an ordinarylumpability-consistent aggregation algorithm, this is not the case with T-lumpability. Based on the axiomatization of Markovian testing and trace equivalences, we provide a sufficient condition for T-lumpability that can easily be embedded in the aggregation algorithm for ordinary lumpability, thus enhancing the potential for exact state space reduction. We also identify a class of systems -those providing incremental services -for which the resulting aggregation algorithm turns out to be useful.

A Two Step Perspective for Kripke Structure Reduction

“…Related work. In the stochastic context, T-Lumpability has been defined over sequential Markovian process calculus (SMPC) [5]. T-Lumpability is defined using four processalgebraic axioms, and allows for a more aggressive state space aggregation than ordinary lumpability.…”

Markovian Testing Equivalence and Exponentially Timed Internal Actions

“…However, they are all meaningful not only from a functional standpoint [17,11,7], but also from a performance standpoint. In fact, Markovian bisimilarity is known to be in agreement with an exact CTMC-level aggregation called ordinary lumpability [14,8], while Markovian testing and trace equivalences are known to be consistent with a coarser exact CTMClevel aggregation called T-lumpability [2,3].…”