Automated verification of dynamic multi-threaded computing systems can be adversely affected by problems relating to dynamic process creation. We therefore investigate - in a general setting of labelled transition systems - a way of reducing the state spaces of multi-threaded systems. At the heart of our method is a state equivalence, which may produce a finite representation of an infinite state system while still allowing to validate the relevant behavioural properties. We demonstrate the feasibility of the method through experiments involving the checking of the proposed state equivalence.