# EECI 2012: Synthesis of Reactive Control Protocols

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This lecture discusses planner synthesis from LTL specification. In particular, we focus on systems that maintain an ongoing interaction with their environment. For the system to be correct, the planner needs to ensure that the specification holds for all the possible behaviors of the environment. This "reactive" system synthesis problem originates from Church's problem formulated in 1965 and can be viewed as a two-person game between the system and the environment. In general, the complexity of reactive system synthesis problem is double exponential. However, for certain special cases, the problem can be solved in polynomial time. We discuss those special cases, with the emphasis on the case where the problem can be formulated as a Generalized Reactivity(1) game.

## Lecture Materials

- Lecture slides: Synthesis of Reactive Control Protocols

## Further Reading

On the development of reactive systems, D. Harel and A. Pnueli, Logics and models of concurrent systems, Springer-Verlag New York, Inc., 1985, pp. 477–498. For discussion about closed and open systems

Logic, arithmetics, and automata, A. Church, Proceedings of the international congress of mathematicians, 1962. An article on Church’s solvability problem [Thanks to Scott Livingston for pointing that all ICM proceedings (and this paper in particular) are available at this link.]

On the synthesis of a reactive module, A. Pnueli and R. Rosner, Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages, 1989. A good reference on reactive module synthesis

Synthesis of reactive(1) designs, N. Piterman, A. Pnueli and Y. Sa’ar, Verification, Model Checking and Abstract Interpretation, Springer, 2006.

## Additional Information

- JTLV project A Framework where GR(1) synthesis is implemented