Well, you can now use this as a tool to show that if you can reduce part of a problem to creating a progression free set you can use that to show the complexity

Well, you can now use this as a tool to show that if you can reduce part of a problem to creating a progression free set you can use that to show the complexity of a problem. The ways I've seen combinatorics (and graph theory!) interact with software engineering is typically showing that a problem is too expensive to solve at scale.