Gröbner bases in TCS? Does anyone know of interesting applications of Gröbner bases to theoretical computer science?

Gröbner bases are used to solve multi-variate polynomial equations, an NP-hard problem in general. I was wondering whether some tractable special cases were used to provide efficient algorithms/constructions/proofs in TCS or TCS-related areas (combinatorics, coding theory).
Gröbner basis computation, while EXPSPACE-complete in general, are in PSPACE over Boolean rings. This has applications in model-checking to replace BDDs: Quoc-Nam Tran, "A PSPACE Algorithm for Groebner Bases Computation in Boolean Rings", Proc. WASET, Vol. 35, Nov. 2008, ISSN 2070-3740

[NOTE] The result stating that Groebner basis computation is in PSPACE over Boolean rings seems wrong, see Mark van Hoeij, Gröbner basis in Boolean rings is not P-SPACE, arXiv:1502.07220, 2015.

[NOTE] The claim that the result stating that Groebner basis computation is in PSPACE over Boolean rings seems wrong, is wrong. The author confuses PSPACE-computability with having a polynomial size. A PSPACE function may well have exponentially long output.