The mixed product gives a global representation of concurerent systems modelled by interacting automata.In this paper we study the opposite operation: we characterise the transition systems which may be viewed as products and we build some of their decompositions.lFor a large subclass of systems,we exhibit a minimal decomposition.We finally extend this study to asynchronous utomata whose componsents may be non-determinstic and present an optimal characterisation of the corresponding transition systems.Thus,we state precisely the shape of the transition systems which are associated to three kinds of system; in that way,we obtain axioms which are similar to those identified for the synthesis problem of Petri nets.
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