Embodiments of the present invention can use a protocol-independent, vendor-independent, efficient and scalable abstraction model for representing the forwarding functionality of networks. Such a model can be used for systematic analysis and verification of networks. Packet header values may be represented as groups of one or more wildcarded bit strings, where unspecified header values are assumed to be fully wildcarded. This representation can describe many combinations of packets in a space-efficient way, enables more efficient tracing and transformation operations, and can even represent traffic from large internet routing tables efficiently. As a result of the scalability benefits of this more effective way to store and operate on packet collections, network modeling can scale to some of the largest, most complicated networks—those where the benefits are the greatest.