Opacity for linear constraint Markov chains

Constraint Markov Chains

Notions of speci cation, implementation, satisfaction, and re nement, together with operators supporting stepwise design, constitute a speci cation theory. We construct such a theory for Markov Chains (MCs) employing a new abstraction of a Constraint MC. Constraint MCs permit rich constraints on probability distributions and thus generalize prior abstractions such as Interval MCs. Linear (polyn...

New results for Constraint Markov Chains

This paper studies compositional reasoning theories for stochastic systems. A specification theory combines notions of specification and implementation with satisfaction and refinement relations, and a set of operators that together support stepwise design. One of the first behavioral specification theories introduced for stochastic systems is the one of Interval Markov Chains (IMCs), which are...

Linear Distances between Markov Chains

We introduce a general class of distances (metrics) between Markov chains, which are based on linear behaviour. This class encompasses distances given topologically (such as the total variation distance or trace distance) as well as by temporal logics or automata. We investigate which of the distances can be approximated by observing the systems, i.e. by black-box testing or simulation, and we ...

Linear Algebra Application~ Markov Chains

Rapidly Mixing Markov Chains for Dismantleable Constraint Graphs

If G = (VG, EG) is an input graph, and H = (VH , EH) a fixed constraint graph, we study the set Ω of homomorphisms (or colorings) from VG to VH , i.e. functions which preserve adjacency. Brightwell and Winkler introduced the notion of dismantleable constraint graph to characterize those H whose set Ω is connected under single vertex recolorings for every G. Given fugacities λ(c) > 0 (c ∈ VH) ou...