Some direct interconnections between formal language theory and discrete-time linear system theory

Abstract

In an attempt to bridge the gap between theoretical computer science and, system theory, three problems from developmental system theory are discussed in parallel with the corresponding problems for discrete-time linear systems. The question of existence of algorithmic solutions to each of the problems is investigated. Based on elementary linear algebra, it is shown that each of the three problems is decidable for discrete-time linear systems while the equivalent problems for developmental systems are either undecidable or the existence of algorithmic solutions is an open problem. Developmental systems are studied in both theoretical biology and formal language theory so the discussion presented in this paper provides some fundamental links between these two subjects and linear systems theory.