Partially Ordered Symbolic Automata (POSAs) are used as the semantical foundation of visual formalisms like the scenario based language of Live Sequence Charts (LSCs). To check whether a model satisfies an LSC requirement, the LSC's POSA can be composed in parallel to the model as an observer automaton or it can be translated to a CTL or LTL formula. Thus by the well-known complexity properties of CTL and LTL model-checking, the size of an LSC's POSA directly contributes to the runtime of the model-checking task. This size grows with the concurrency allowed by the LSC, e.g. when the observation order of LSC elements is relaxed by enclosing them in a coregion. We investigate decomposition properties of POSAs with deterministic states, i.e. states with disjointly annotated outgoing transitions. We devise a procedure to decompose a POSA with deterministic states into a set of POSAs whose intersection language is equal to the language of the original POSA. When decomposing at dom...