Synthesis over Regularly Approximable Data Domains

We study reactive synthesis of systems interacting with environments using infinite alphabets. Register automata and transducers are popular formalisms for specifying and modelling such systems. They extend finite-state automata by adding registers to store data values and to compare the incoming data values against stored ones. Synthesis from nondeterministic or universal register automata is undecidable in general. Its register-bounded variant, where additionally a bound on the number of registers in a sought transducer is given, is however known to be decidable for universal register automata which can compare data for