This paper discusses a result by Fliess about input-output equations for polynomial systems with time delays, and strengthens the result somewhat. The proof given is more detailed and opens the way for constructive methods for determining the input-output behavior. Some such methods based on Gröbner bases are described in detail. Furthermore, some connections with observability are exploited.
Keywords: delay systems, difference-differential equations, commutative algebra, field theory, difference-differential algebra, elimination theory, implicitization.