Automata Column

Abstract

In this issue, the automata column discusses a powerful decision procedure for infinite state systems, which I would call the Hilbert Method, because it uses theorems like Hilbert's Basis Theorem or the Nullstellensatz. The method - which reduces combinatorial objects like words or trees to algebraic objects like numbers and polynomials - has been used to solve important open problems like: Ehrenfeucht's Conjecture, the equivalence problem for HDT0L systems, or the equivalence problem for tree-to-string transducers. Because of its power, generality and simplicity, I think that the method should become a standard part of the toolkit of automata theory for working with infinite state systems, joining established methods like integer programming or well-structured transition systems.