Synthesis from Knowledge - Based Speci cations ? ( Extended

In program synthesis, we transform a speciication into a program that is guaranteed to satisfy the speciication. In synthesis of reactive systems, the environment in which the program operates may behave nondeterministically, e.g., by generating diierent sequences of inputs in diierent runs of the system. To satisfy the speciication, the program needs to act so that the speciication holds in every computation generated by its interaction with the environment. Often, the program cannot observe all attributes of its environment. In this case, we should transform a speciication into a program whose behavior depends only on the observable history of the computation. This is called synthesis with incomplete information. In such a setting, it is desirable to have a knowledge-based speciication, which can refer to the uncertainty the program has about the environment's behavior. In this work we solve the problem of synthesis with incomplete information with respect to speciications in the logic of knowledge and time. We show that the problem has the same worst-case complexity as synthesis with complete information.