A series of considerations is developed to argue that differential-algebraic decision methods could become useful tools for some system theory approaches. Throughout the paper, previous works of J. F. Ritt, R. A. Kolchin, and A.  Rosenfeld  are extensively invoked.

Some preliminary definitions concerning differential polynomial algebras are given in the first section, followed by a series of results on well-ordering and reduction. The concepts of reduced and coherent autoreduced sets are presented in Sections 2.3 and 2.4. A reduction procedure and the Ritt algorithm for the construction of the characteristic sets are presented in Sections 2.3 and 2.5.1. The third section of the paper is devoted to the differential dimension polynomial; Diop argues that this concept could provide a better base for the size of a system than the differential transcendence degree of the differential algebra associated with such a system. Next, some basic decision problems, such as prime component decomposition, membership, and elimination, are briefly considered. A series of possible applications of differential algebraic decision methods to system theory is supplied in the final part of the paper. The discussion focuses on computation of invariants, minimal realization of an ordinary irreducible system, and tests of observability and invertibility. According to the author, more applications are expected.

The author uses some fundamental works in differential algebraic decision methods for applications in system theory. This research is mainly of theoretical interest.