Compositional Minimal Semantics for the Stochastic Process Algebra Tipp

The problem of deriving the Markov chain underlying a stochastic process algebra term is addressed. Transition rate matrices are used as a convenient method for uniquely describing Markov chains. For a modiied version of the stochastic process algebra TIPP, we propose a set of new semantic rules which specify the way in which process terms are translated into their corresponding matrices. For each operator of the language, a semantic rule describes how the (one ore more) operand matrices have to be combined in order to form the matrix corresponding to the overall term. These semantic rules guarantee certain highly advantageous properties of the resulting matrices, the two most important of which are (i) the absence of non-reachable states and (ii) minimality with respect to Markov chain lumpability. Thus avoiding redundancy, our new approach is a contribution to the struggle against state space explosion.