Efficient handling of obligation constraints in synthesis from omega-regular specifications

A finite state reactive system (for instance a hardware controller) can be specified through a set of ω-regular properties, most of which are often safety properties. In the game-based approach to synthesis, the specification is converted to a game between the system and the environment. A deterministic implementation is obtained from the game graph and a system´s winning strategy. However, there are obstacles to extract an efficient implementation from the game in hardware. On the one hand, a large space must be explored to find a strategy that has a concise representation. On the other hand, the transition structure inherited from the game graph may correspond to a state encoding that is far from optimal. In the approach presented in this paper, the game is formulated as a sequence of Boolean equations. That leads to significant improvements in the quality of the implementation compared to existing automata-based techniques. It is also shown discussed to extend this approach to the synthesis from obligation properties.