Designing Theory of Computing Backwards

The design of any technical Computer Science course must involve its context within the institution's CS program, but also incorporate any new material that is relevant and appropriately accessible to students. In many institutions, theory of computing (ToC) courses within undergraduate CS programs are often placed near the end of the program, and have a very common structure of building off previous sections of the course. The central question behind any such course is ``What are the limits of computers?'' for various types of computational models. However, what is often intuitive for students about what a ``computer'' is--a Turing machine--is taught at the end of the course, which necessitates motivation for earlier models. This poster contains our experiences in designing a ToC course that teaches the material effectively ``backwards,'' with pedagogic motivation of instead asking the question ``What suitable restrictions can we place on computers to make their problems tractable?'' We also give recommendations for future course design.