We call network of automata a family of partially synchronised automata, i.e. a family of deterministic automata which are synchronised via shared letters, and evolve independently otherwise. We address the problem of uniform random sampling of words recognised by a network of automata. To that purpose, we define the reduced automaton of the model, which involves only the product of the synchronised part of the component automata. We provide uniform sampling algorithms which are polynomial with respect to the size of the reduced automaton, greatly improving on the best known algorithms. Our sampling algorithms rely on combinatorial and probabilistic methods and are of three different types: exact, Boltzmann and Parry sampling.

For a large Markovian model, a “product form” is an explicit description of the steady-state behaviour which is otherwise generally untractable. Being first introduced in queueing networks, it has been adapted to Markovian Petri nets. Here we address

Consider a Markovian Petri net with race policy. The marking process has a “product form” stationary distribution if the probability of viewing a given marking can be decomposed as the product over places of terms depending only on the local marking.

We consider a system of uniform recurrence equations of dimension 1 and we show how its computation can be carried out using minimal memory size with several synchronous processors. This result is then applied to register minimization for digital circuits and parallel computation of task graphs.