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We demonstrate the first Recurrent Neural Network architecture for learning Signal Temporal Logic formulas, and present the first systematic comparison of formula inference methods. Legacy systems embed much expert knowledge which is not explicitly formalized. There is great interest in learning formal specifications that characterize the ideal behavior of such systems -that is, formulas in temporal logic that are satisfied by the system's output signals. Such specifications can be used to better understand the system's behavior and improve design of its next iteration. Previous inference methods either assumed certain formula templates, or did a heuristic enumeration of all possible templates. This work proposes a neural network architecture that infers the formula structure via gradient descent, eliminating the need for imposing any specific templates. It combines learning of formula structure and parameters in one optimization. Through systematic comparison, we demonstrate that this method achieves similar or better mis-classification rates (MCR) than enumerative and lattice methods. We also observe that different formulas can achieve similar MCR, empirically demonstrating the underdeterminism of the problem of temporal logic inference.

We address the problem of maintaining resource availability in a networked multi-robot system performing distributed target tracking. In our model, robots are equipped with sensing and computational resources enabling them to track a target's position using a Distributed Kalman Filter (DKF). We use the trace of each robot's sensor measurement noise covariance matrix as a measure of sensing quality. When a robot's sensing quality deteriorates, the systems communication graph is modified by adding edges such that the robot with deteriorating sensor quality may share information with other robots to improve the team's target tracking ability. This computation is performed centrally and is designed to work without a large change in the number of active communication links. We propose two mixed integer semi-definite programming formulations (an 'agent-centric' strategy and a 'team-centric' strategy) to achieve this goal. We implement both formulations and a greedy strategy in simulation and show that the teamcentric strategy outperforms the agent-centric and greedy strategies.

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