Lazy Synthesis

We present an automatic method for the synthesis of processes in a reactive system from specifications in linear-time temporal logic (LTL). The synthesis algorithm executes a loop consisting of three phases: Solve, Check, and Refine. In the Solve phase, a candidate solution is obtained as a model of a Boolean constraint system; in the Check phase, the candidate solution is checked for reachable error states; in the Refine phase, the constraint system is refined to eliminate any errors found in the Check phase. The algorithm terminates when an implementation without errors is found. We call our approach "lazy," because constraints on possible process implementations are only considered incrementally, as needed to rule out incorrect candidate solutions. This contrasts with the standard "eager" approach, where the full specification is considered right away. We report on experience in the arbiter synthesis for the AMBA bus protocol, where lazy synthesis leads to significantly smaller implementations than the previous eager approach.