Quotient Machines, the Interface Equation and Protocol Conversion

A major problem in protocol engineering is the derivation of the specification of a converter which mediates between two different protocols. This paper describes a technique which melds together automata theory and topology, and which has achieved a major efficiency gain over current methods for automatic converter synthesis in that it has been able to deal with protocols that are larger than those dealt with in previous work. The technique is based on an equation of process algebra known as the interface equation, and utilizes topological graph theory to solve it. We provide a simplified view of the interface equation and show how its solution can be transformed into the process of deriving a quotient graph. The paper ends with a discussion of the industrial implications of our work and an analysis of our algorithm.