Showing papers by "Bernard P. Zeigler published in 1972"
TL;DR: Sufficient condit ions are given under which preserva of the local s ta te space s t ruc tu re (weak morphism) also forces the preserva t ion of component in teract ion and provides a ra t ionale for making valid inferences about the local local dynamic of a sys tem when the model of a behaviora l ly val id model is known.
Abstract: A s imula t ion consists of a tr iple of au toma ta (system to be s imulated, model of this system, computer realizing the model). In a val id s imulat ion these elements are connected by behavior and s t ruc ture preserving morphisms. In format iona l and complexity considerat ions mot iva te the development of s t ruc tu re preserving morphisms which can preserve not only global, bu t also local dynamic s t ruc ture . A formalism for au tomaton s t ruc tu re ass ignment and the re levant weak and s t rong s t ruc tu re preserving morphisms are introduced. I t is shown tha t these preserva t ion not ions proper ly refine the usual au tomaton homomorphism concepts. Sufficient condit ions are given under which preserva t ion of the local s ta te space s t ruc tu re (weak morphism) also forces the preserva t ion of component in teract ion. The s t rong sense in which these condit ions are necessary is also demons t ra ted . This provides a ra t ionale for making valid inferences about the local s t ruc ture of a sys tem when t h a t of a behaviora l ly val id model is known.
51 citations
TL;DR: A strengthened version of the conjecture that a certain complexity measure involving the size of the strong components of a logical net formed a hierarchy for net behavior is proved by establishing that any logical net can be interpreted as a series-parallel composition of nets associated with its strong components.
Abstract: In a foundational paper on the theory of automata A. W. Burks and H. Wang (1957) conjectured that a certain complexity measure involving the size of the strong components of a logical net formed a hierarchy for net behavior. This conjecture was established by Rhodes and Krohn. In this paper a strengthened version of the conjecture is proved by establishing that any logical net can be interpreted as a series-parallel composition of nets associated with its strong components. Some properties of the periodic behavior of machines, shown to be preserved under simulation and composition operations, are used to complete the proof. The relationship of this approach to algebraic proofs of series-parallel irreducibility is discussed.