Estimator-based reactive synthesis under incomplete information

Lack of complete run-time information about the environment behavior significantly increases the computational complexity and limits the applicability of practical reactive synthesis methods, e.g., synthesis from generalized reactivity( 1) specifications. We tackle this difficulty by splitting incomplete-information controller synthesis into estimator construction and complete-information synthesis steps. The estimator, which executes in parallel to the controller, establishes approximations of the unobserved variables that are salient for the synthesis step. It essentially provides an abstraction from the belief space of the controller, whose exponential growth often plagues incomplete-information synthesis, by keeping track of only the properties of relevance for the specification engineer and the scenario under consideration.

We formalize an estimator notion for controller synthesis, and present a framework in which such estimators work in concert with controllers reacting partly to the estimator outputs to realize given temporal logic specifications. In order to limit the size and structure of the estimators, we focus on positional estimators in computation. Moreover, we demonstrate how such estimators are well-suited to be used in the context of generalized reactivity(1) synthesis. We illustrate the use of the estimator-based synthesis method on a running example motivated by intelligent transportation systems.