Automated verification of dynamic multi-threaded computing systems is severely affected by problems relating to dynamic process creation. In this paper, we describe an abstraction technique aimed at generating reduced state space representations for such systems. To make the new technique applicable to a wide range of different system models, we express it in terms of general labelled transition systems. At the heart of our technique is an equivalence relation on system states based on a suitable isomorphism between their component parts and relationships between component process identifiers. In addition, the equivalence takes into account new process identifiers which can be derived from those present in the states being compared, in effect performing a limited lookahead. Applying state space reduction based on such a state equivalence may produce a finite representation of an infinite state system while still allowing to validate essential behavioural properties, e.g., freedom from deadlocks. We evaluate the feasibility of the proposed method through extensive experiments. The results clearly demonstrate that the new state space reduction technique can be implemented in an efficient way. We also describe how the new state equivalence relation can be implemented for a class of high-level Petri nets supporting dynamic thread creation.