# Differential Bisimulation for a Markovian Process Algebra

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)

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## Abstract

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.

Item Type: Book Section 10.1007/978-3-662-48057-1_23 QUANTICOL Q Science > QA Mathematics > QA75 Electronic computers. Computer science Computer Science and Applications Caterina Tangheroni 12 Feb 2016 12:37 12 Feb 2016 12:37 http://eprints.imtlucca.it/id/eprint/3063