Reducing the computational effort of symbolic supervisor synthesis

Supervisor synthesis is a means to algorithmically derive a supervisory controller from a discrete-event model of a system and a requirements specification. For large systems, synthesis suffers from state space explosion. To mitigate this, synthesis can be applied to a symbolic representation of the models by using Binary Decision Diagrams (BDDs). Peak used BDD nodes and BDD operation count are introduced as deterministic and platform independent metrics to express the computational effort of a symbolic synthesis. These BDD-based metrics are useful to analyze the efficiency of the synthesis algorithm. From this analysis, modifications can be made to how BDDs are handled during synthesis, improving synthesis efficiency. We demonstrate this approach by introducing and analyzing: DCSH, a variable ordering heuristic; several edge ordering heuristics; and an approach to efficiently enforce state exclusion requirements in synthesis. These methods were recently implemented in our open source supervisory control tool: Eclipse ESCET. The analysis is based on large scale experiments of performing synthesis on a variety of models from literature. We show that: (1) by using DCSH, synthesis with high computational effort can be avoided, and generally low computational effort is required, relative to the variable ordering heuristics that were used prior to this work; (2) applying reverse-model edge order realizes relatively low synthesis effort; and (3) state exclusion requirements can efficiently be enforced by restricting edge guards prior to synthesis. While these methods reduce computational effort in practice, it should be noted that they do not affect the theoretical (worst-case) complexity of synthesis.