Finite state automata (FSA) are used by many network processing applications to match complex sets of regular expressions in network packets. In order to make FSA-based matching possible even at the ever-increasing speed of modern networks, multi-striding has been introduced. This technique increases input parallelism by transforming the classical FSA that consumes input byte by byte into an equivalent one that consumes input in larger units. However, the algorithms used today for this transformation are so complex that they often result unfeasible for large and complex rule sets. This paper presents a set of new algorithms that extend the applicability of multi-striding to complex rule sets. These algorithms can transform nondeterministic finite automata (NFA) into their multi-stride form with reduced memory and time requirements. Moreover, they exploit the massive parallelism of graphical processing units for NFA-based matching. The final result is a boost of the overall processing speed on typical regex-based packet processing applications, with a speedup of almost one order of magnitude compared to the current state-of-the-art algorithms.