Synthesis over Regularly Approximable Data Domains [article]

Léo Exibard, Emmanuel Filiot, Ayrat Khalimov
2021 arXiv   pre-print
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
more » ... ters in a sought transducer is given, is however known to be decidable for universal register automata which can compare data for equality. In this paper, we generalise this result. We introduce the notion of ω-regularly approximable data domains, and show that register-bounded synthesis from universal register automata on such domains is decidable. Importantly, the data domain (ℕ, =, <) with natural order is ω-regularly approximable, and its closer examination reveals that the synthesis problem is decidable in time doubly exponential in the number of registers, matching the known complexity of the equality-only case (ℕ, =). We then introduce a notion of reducibility between data domains which we exploit to show decidability of synthesis over, e.g., the domains (ℕ^d, =^d, <^d) of tuples of numbers equipped with the component-wise partial order and (Σ^*, =, ≺) of finite strings with the prefix relation.
arXiv:2105.09978v3 fatcat:xyb2whrphncgnlit2omn2up2fm