On a Probabilistic Chemical Abstract Machine and the Expressiveness of Linda Languages

  • Alessandra Di Pierro
  • Chris Hankin
  • Herbert Wiklicky
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4111)


The Chemical Abstract Machine (CHAM) of Berry and Boudol provides a commonly accepted, uniform framework for describing the operational semantics of various process calculi and languages, such as for example CCS, the π calculus and coordination languages like Linda. In its original form the CHAM is purely non-deterministic and thus only describes what reactions are possible but not how long it will take (in the average) before a certain reaction takes place or its probability. Such quantitative information is however often vital for “real world” applications such as systems biology or performance analysis. We propose a probabilistic version of the CHAM. We then define a linear operator semantics for the probabilistic CHAM which exploits a tensor product representation for distributions over possible solutions. Based on this we propose a novel approach towards comparing the expressive power of different calculi via their encoding in the probabilistic CHAM. We illustrate our approach by comparing the expressiveness of various Linda Languages.


Tensor Product Operator Semantic Expressive Power Rule Operator Discrete Time Markov Chain 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Alessandra Di Pierro
    • 1
  • Chris Hankin
    • 2
  • Herbert Wiklicky
    • 2
  1. 1.Dipartimento di InformaticaUniversity of PisaItaly
  2. 2.Department of ComputingImperial College LondonUK

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