  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 under-determinism of the
problem of temporal logic inference.
