Synthesis with Identifiers

We consider the synthesis of reactive systems from specifications with identifiers. Identifiers are useful to parametrize the input and output of a reactive system, for example, to state which client requests a grant from an arbiter, or the type of object that a robot is expected to fetch. Traditional reactive synthesis algorithms only handle a constant bounded range of such identifiers. However, in practice, we might not want to restrict the number of clients of an arbiter or the set of object types handled by a robot a priori. We first present a concise automata-based formalism for specifications with identifiers. The synthesis problem for such specifications is undecidable. We therefore give an algorithm that is always sound, and complete for unrealizable safety specifications. Our algorithm is based on computing a pattern-based abstraction of a synthesis game that captures the realizability problem for the specification. The abstraction does not restrict the possible solutions to finite-state ones and captures the obligations for the system in the synthesis game. We present an experimental evaluation based on a prototype implementation that shows the practical applicability of our algorithm.