Synthesis of Interface Automata

We investigate the problem of synthesising an interface automaton R such that P ‖ R Q, for given deterministic interface automata P and Q. We show that a solution exists iff P and Q⊥ are compatible, and the most general solution is given by (P ‖ Q⊥)⊥, where P⊥ is the automaton P with inputs and outputs interchanged. We also characterise solutions in terms of winning input strategies in the automaton (P ⊗Q⊥)⊥, and the most general solution in terms of the most permissive winning strategy. We apply the synthesis problem for interfaces to the problem of synthesising converters for mismatched protocols.