Quantitative Assume Guarantee Synthesis

In assume-guarantee synthesis, we are given a specification \(\langle A,G \rangle \), describing an assumption on the environment and a guarantee for the system, and we construct a system that interacts with an environment and is guaranteed to satisfy G whenever the environment satisfies A. While assume-guarantee synthesis is 2EXPTIME-complete for specifications in LTL, researchers have identified the \(\text {GR(1)}\) fragment of LTL, which supports assume-guarantee reasoning and for which synthesis has an efficient symbolic solution. In recent years we see a transition to quantitative synthesis, in which the specification formalism is multi-valued and the goal is to generate high-quality systems, namely ones that maximize the satisfaction value of the specification.