Constraint Markov Chains

Benoit Caillaud (1) , Benoît Delahaye (1) , Kim Guldstrand Larsen (2) , Axel Legay (1) , Mikkel L. Pedersen (2) , Andrzej Wasowski (3)

1 S4 - System synthesis and supervision, scenarios
2 AAU - Aalborg University [Denmark]
3 ITU - IT University of Copenhagen

Notions of specification, implementation, satisfaction, and refinement, together with operators supporting stepwise design, constitute a specification 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 (polynomial) constraints suffice for closure under conjunction (respectively parallel composition). This is the first specification theory for MCs with such closure properties. We discuss its relation to simpler operators for known languages such as probabilistic process algebra. Despite the generality, all operators and relations are computable.

Mots clés: Specification theory; Markov Chains; Compositional reasoning; Abstraction; Process algebra

Domaines: Autre [cs.OH]

Benoit Caillaud, Benoît Delahaye, Kim Guldstrand Larsen, Axel Legay, Mikkel L. Pedersen, et al.. Constraint Markov Chains. Theoretical Computer Science, 2011, 412 (34), pp.4373-4404. ⟨10.1016/j.tcs.2011.05.010⟩. ⟨hal-00654003⟩