As a project in the Professor Nagpaul Fellowship, I presented a paper on the 'The Road Coloring Problem' conjectured by Roy Adler and Benjamin Weiss (1970) and proved by Avraham Trahtman(2009).
The aim of this project was to undertand the Road Coloring Theorem, recreate the paper, present it in an accessible manner with a python implementation. The real life application of the project was to take the the roads around campus as edges and several landmarks as nodes. The problem deals with finding the synchronising coloring for a graph following certain properties, such that no matter which node on the graph you start from , you shall always reach the same destination if you follow the coloring.
In the context of an automaton, a synchronizing sequence makes it resistant to input errors, since the sequence can be used to reset the automaton back to the required state no matter where the error occurred.