Family of 4-phase latch protocols

A complete family of untimed asynchronous 4-phase pipeline protocols is derived and characterised. This family contains all untimed protocols where data becomes valid before the request signal rises. Starting with a specification of the most parallel such protocol, rules are provided for concurrency reduction to systematically generate the family of all 137 related protocols that can be pipelined. Graphical and textual nomenclatures are developed to represent protocol properties and behaviours. The protocols are categorised according to their behaviours when composed into linear and structured parallel pipelines. Six basic categories emerge, along with several properties such as a single state that determines whether a protocol is fully or half buffered. When equivalence classes are calculated for parallel pipeline behaviours they are dominated by 15 shapes (all of which are delay-insensitive) which are related by a simple lattice. Several published circuits are shown to map to 16 of our 137 family members. This work enhances the understanding of handshake protocols, their properties, and relationships between different implementations in terms of concurrency and behavioural properties.