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Reward based congruences: Can we aggregate more? (English) Zbl 1007.68132
De Alfaro, Luca (ed.) et al., Process algebra and probabilistic methods. Performance modelling and verification. Joint international workshop, PAPM-PROBMIV 2001, Aachen, Germany, September 12-14, 2001. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 2165, 136-151 (2001).
Summary: In this paper we extend a performance measure sensitive Markovian bisimulation congruence based on yield and bonus rewards that has been previously defined in the literature, in order to aggregate more states and transitions while preserving compositionality and the values of the performance measures. The extension is twofold. First, we show how to define a performance measure sensitive Markovian bisimulation congruence that aggregates bonus rewards besides yield rewards. This is achieved by taking into account in the aggregation process the conditional execution probabilities of the transitions to which the bonus rewards are attached. Second, we show how to define a performance measure sensitive Markovian bisimulation congruence that allows yield rewards and bonus rewards to be used interchangeably up to suitable correcting factors, aiming at the introduction of a normal form for rewards. We demonstrate that this is possible in the continuous time case, while it is not possible in the discrete time case because compositionality is lost.
For the entire collection see [Zbl 0971.00028].

MSC:
68Q85 Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
68Q60 Specification and verification (program logics, model checking, etc.)
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