Reward Based Congruences: Can We Aggregate More?

  • Marco Bernardo
  • Mario Bravetti
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2165)


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.


Composition Operator Operational Semantic Priority Level Time Case Passive Action 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Marco Bernardo
    • 1
  • Mario Bravetti
    • 2
  1. 1.Dipartimento di InformaticaUniversità di TorinoTorinoItaly
  2. 2.Dipartimento di Scienze dell’InformazioneUniversità di BolognaBolognaItaly

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