Abstract
We consider Stochastic Automata Networks whose transition rates depend on the whole system state but are not synchronised and are restricted to satisfy a property called inner proportional.We prove that this class of SANs has both product form steady-state distribution and product form probability over untimed paths. This product form result is then applied to check formulae that are equivalent to some special structure that we call path-product of sets of untimed paths. In particular, we show that product form solutions can be used to check unbounded Until formulae of the Continuous Stochastic Logic.
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Acknowledgments
The authors thank to Jean-Michel Fourneau for the fruitful discussions on product form solutions of SANs.
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© 2013 Springer-Verlag London
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Pekergin, N., Tran, MA. (2013). Compositional Verification of Untimed Properties for a Class of Stochastic Automata Networks. In: Gelenbe, E., Lent, R. (eds) Computer and Information Sciences III. Springer, London. https://doi.org/10.1007/978-1-4471-4594-3_11
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DOI: https://doi.org/10.1007/978-1-4471-4594-3_11
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