Summary: Signal Transition Graphs (STG) are a formalism for the description of asynchronous circuit behaviour. In this paper we propose (and justify) a formal semantics of non-deterministic STGs with dummies and OR-causality. For this, we introduce the concept of output-determina\-cy, which is a relaxation of determinism, and argue that it is reasonable and useful in the speed-independent context. We apply the developed theory to improve an STG decomposition algorithm used to tackle the state explosion problem during circuit synthesis, and present some experimental data for this improved algorithm and some benchmark examples.