relation: http://eprints.imtlucca.it/3063/
title: Differential Bisimulation for a Markovian Process Algebra
creator: Iacobelli, Giulio
creator: Tribastone, Mirco
creator: Vandin, Andrea
subject: QA75 Electronic computers. Computer science
description: Formal languages with semantics based on ordinary differential equations (ODEs) have emerged as a useful tool to reason about large-scale distributed systems. We present differential bisimulation, a behavioral equivalence developed as the ODE counterpart of bisimulations for languages with probabilistic or stochastic semantics. We study it in the context of a Markovian process algebra. Similarly to Markovian bisimulations yielding an aggregated Markov process in the sense of the theory of lumpability, differential bisimulation yields a partition of the ODEs underlying a process algebra term, whereby the sum of the ODE solutions of the same partition block is equal to the solution of a single (lumped) ODE. Differential bisimulation is defined in terms of two symmetries that can be verified only using syntactic checks. This enables the adaptation to a continuous-state semantics of proof techniques and algorithms for finite, discrete-state, labeled transition systems. For instance, we readily obtain a result of compositionality, and provide an efficient partition-refinement algorithm to compute the coarsest ODE aggregation of a model according to differential bisimulation.
publisher: Springer
date: 2015
type: Book Section
type: PeerReviewed
identifier:   Iacobelli, Giulio and Tribastone, Mirco and Vandin, Andrea  Differential Bisimulation for a Markovian Process Algebra.   In:  Mathematical Foundations of Computer Science 2015. 40th International Symposium, MFCS 2015, Milan, Italy, August 24-28, 2015, Proceedings, Part I.   Lecture Notes in Computer Science  (9234).  Springer, pp. 293-306.  ISBN 978-3-662-48056-4      (2015)  
relation: http://link.springer.com/chapter/10.1007%2F978-3-662-48057-1_23
relation: 10.1007/978-3-662-48057-1_23