Compositional Verification of Untimed Properties for a Class of Stochastic Automata Networks
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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.
KeywordsStochastic Automata Networks Product Form Solution Product Form Steady State Distribution Continuous Stochastic Logic (CSL) Probabilistic Computational Tree Logic (PCTL)
The authors thank to Jean-Michel Fourneau for the fruitful discussions on product form solutions of SANs.
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