# Supervisory control and reactive synthesis: a comparative introduction

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## Abstract

This paper presents an introduction to and a formal connection between synthesis problems for discrete event systems that have been considered, largely separately, in the two research communities of *supervisory control* in control engineering and *reactive synthesis* in computer science. By making this connection mathematically precise in a paper that attempts to be as self-contained as possible, we wish to introduce these two research areas to non-expert readers and at the same time to highlight how they can be bridged in the context of classical synthesis problems. After presenting general introductions to supervisory control theory and reactive synthesis, we provide a novel reduction of the basic supervisory control problem, non-blocking case, to a problem of reactive synthesis with plants and with a maximal permissiveness requirement. The reduction is for fully-observed systems that are controlled by a single supervisor/controller. It complements prior work that has explored problems at the interface of supervisory control and reactive synthesis. The formal bridge constructed in this paper should be a source of inspiration for new lines of investigation that will leverage the power of the synthesis techniques that have been developed in these two areas.

## Keywords

Supervisory control Reactive synthesis Non-blockingness Maximal permissiveness## Notes

### Acknowledgments

We would like to thank Orna Kupferman, Madhusudan Parthasarathy, and John Thistle, for a number of interesting discussions, and Dror Fried for a careful reading of an earlier version of the paper. We also thank the anonymous reviewers for their pertinent comments.

## Supplementary material

## References

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