1. E.D. Sontag. On linear systems and noncommutative rings. Math. Systems Theory, 9(4):327-344, 1975. [PDF] Keyword(s): systems over rings. Abstract:

   This paper studies some problems appearing in the extension of the theory of linear dynamical systems to the case in which parameters are taken from noncommutative rings. Purely algebraic statements of some of the problems are also obtained. Through systems defined by operator rings, the theory of linear systems over rings may be applied to other areas of automata and control theory; several such applications are outlined.




2. E.D. Sontag. On some questions of rationality and decidability. J. Comput. System Sci., 11(3):375-381, 1975. [PDF] Keyword(s): theory of computing and complexity. Abstract:

   Some results are given in the theory of rational power series over a broad class of semirings. In particular, it is shown that for unambiguous sets the notion of rationality is independent of the semiring over which representations are defined. The undecidability of the rationality of probabilistic word functions is also established.

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