Adaptive Reactive Synthesis for LTL and LTLf Modulo Theories

Reactive synthesis is the process of generate correct controllers from temporal logic specifications. Typically, synthesis is restricted to Boolean specifications in LTL. Recently, a Boolean abstraction technique allows to translate LTLT specifications that contain literals in theories into equi-realizable LTL specifications, but no full synthesis procedure exists yet. In synthesis modulo theories, the system receives valuations of environment variables (from a first-order theory T) and outputs valuations of system variables from T. In this paper, we address how to syntheize a full controller using a combination of the static Boolean controller obtained from the Booleanized LTL specification together with on-the-fly queries to a solver that produces models of satisfiable existential T formulae. This is the first synthesis method for LTL modulo theories. Additionally, our method can produce adaptive responses which increases explainability and can improve runtime properties like performance. Our approach is applicable to both LTL modulo theories and LTLf modulo theories.