Weighted lumpability on markov chains

Authors:
Arpit Sharma;Joost-Pieter Katoen
Affiliations:
Software Modeling and Verification Group, RWTH Aachen University, Germany;Software Modeling and Verification Group, RWTH Aachen University, Germany
Venue:
PSI'11 Proceedings of the 8th international conference on Perspectives of System Informatics
Year:
2011

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Abstract

This paper reconsiders Bernardo's T-lumpability on continuous-time Markov chains (CTMCs). This notion allows for a more aggressive state-level aggregation than ordinary lumpability. We provide a novel structural definition of (what we refer to as) weighted lumpability, prove some elementary properties, and investigate its compatibility with linear real-time objectives. The main result is that the probability of satisfying a deterministic timed automaton specification coincides for a CTMC and its weigthed lumped analogue. The same holds for metric temporal logic formulas.