Abstract We present a method for automatically building diagrams for olympiad-level geometry problems and implement our approach in a new open-source software tool, the Geometry Model Builder (GMB). Central to our method is a new domain-specific language, the Geometry Model-Building Language (GMBL), for specifying geometry problems along with additional metadata useful for building diagrams. A GMBL program specifies (1) how to parameterize geometric objects (or sets of geometric objects) and initialize these parameterized quantities, (2) which quantities to compute directly from other quantities, and (3) additional constraints to accumulate into a (differentiable) loss function. A GMBL program induces a (usually) tractable numerical optimization problem whose solutions correspond to diagrams of the original problem statement, and that we can solve reliably using gradient descent. Of the 39 geometry problems since 2000 appearing in the International Mathematical Olympiad, 36 can be expressed in our logic and our system can produce diagrams for 94% of them on average. To the best of our knowledge, our method is the first in automated geometry diagram construction to generate models for such complex problems.

Software engineering involves writing new code or editing existing code. Recent efforts have investigated the neural processes associated with reading and comprehending code --- however, we lack a thorough understanding of the human cognitive processes underlying code writing. While prose reading and writing have been studied thoroughly, that same scrutiny has not been applied to code writing. In this paper, we leverage functional brain imaging to investigate neural representations of code writing in comparison to prose writing. We present the first human study in which participants wrote code and prose while undergoing a functional magnetic resonance imaging (fMRI) brain scan, making use of a full-sized fMRI-safe QWERTY keyboard.

Data structures permeate many aspects of software engineering, but their associated human cognitive processes are not thoroughly understood. We leverage medical imaging and insights from the psychological notion of spatial ability to decode the neural representations of several fundamental data structures and their manipulations. In a human study involving 76 participants, we examine list, array, tree, and mental rotation tasks using both functional near-infrared spectroscopy (fNIRS) and functional magnetic resonance imaging (fMRI). We find a nuanced relationship: data structure and spatial operations use the same focal regions of the brain but to different degrees. They are related but distinct neural tasks. In addition, more difficult computer science problems induce higher cognitive load than do problems of pure spatial reasoning. Finally, while fNIRS is less expensive and more permissive, there are some computing-relevant brain regions that only fMRI can reach.