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 (polynomial) constraints su ce for closure under conjunction (respectively parallel composition). This is the rst speci cation 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.