Weighted probabilistic equivalence preserves ω-regular properties

Authors:
Arpit Sharma
Affiliations:
Software Modeling and Verification Group, RWTH Aachen University, Germany
Venue:
MMB'12/DFT'12 Proceedings of the 16th international GI/ITG conference on Measurement, Modelling, and Evaluation of Computing Systems and Dependability and Fault Tolerance
Year:
2012

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Abstract

Equivalence relations can be used to reduce the state space of a system model, thereby permitting more efficient analysis. This paper extends the notion of weighted lumpability (WL) defined on continuous-time Markov chains (CTMCs) to the discrete-time setting, i.e., discrete-time Markov chains (DTMCs). We provide a structural definition of weighted probabilistic equivalence (WPE), define the quotient under WPE and prove some elementary properties. We show that ω-regular properties are preserved when reducing the state space of a DTMC using WPE. Finally, we show that WPE is compositional w.r.t. synchronous parallel composition.