# Reactive Synthesis: Towards Output-Sensitive Algorithms

Bernd Finkbeiner and Felix Klein

Reactive synthesis is a technology for the automatic construction of reactive systems from logical specifications. In these lecture notes, we study different algorithms for the reactive synthesis problem of linear-time temporal logic (LTL). The classic game-based synthesis algorithm is input-sensitive in the sense that its performance is asymptotically optimal in the size of the specification, but it produces implementations that may be larger than necessary. We contrast this algorithm with output-sensitive algorithms for reactive synthesis, i.e., algorithms that are optimized towards the size or structural complexity of the synthesized system. We study the bounded synthesis algorithm, which produces an implementation with a minimal number of states, and the bounded cycle synthesis algorithm, which additionally guarantees that the number of cycles of the implementation is minimal.