Protocol converter synthesis by solving language equations

We address the problem of protocol converter synthesis, i.e., the automatic design of automata to translate between different protocols, by means of the definition and solution of equations defined over regular languages and finite automata/finite state machines (FSMs). The protocol conversion problem has been discussed in an extensive literature which assumes a variety of modeling frames, from supervisory control of discrete event systems to input-output automata and interfaces. In this paper, we model it by parallel language equations, whose largest solution includes all protocol converters that solve the problem; this is a strong advantage over computational techniques that deliver only one or a few solutions, leading to inferior implementations. Our model is versatile, because it can handle different topologies and constraints on the solutions. We extended a software package to enable it to solve parallel equations. As an example we model and solve a classical protocol mismatch problem.