%0 Book Section
%A Iacobelli, Giulio
%A Tribastone, Mirco
%A Vandin, Andrea
%B Mathematical Foundations of Computer Science 2015. 40th International Symposium, MFCS 2015, Milan, Italy, August 24-28, 2015, Proceedings, Part I
%D 2015
%F eprints:3063
%I Springer
%N 9234
%P 293-306
%S Lecture Notes in Computer Science
%T Differential Bisimulation for a Markovian Process Algebra
%U http://eprints.imtlucca.it/3063/
%X 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.