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Full Description
Discrete-Time and Discrete-Space Dynamical Systems provides a systematic characterization of the similarities and differences of several types of discrete-time and discrete-space dynamical systems, including:
Boolean control networks;
nondeterministic finite-transition systems;
finite automata;
labelled Petri nets; and
cellular automata.
The book's perspective is primarily based on topological properties though it also employs semitensor-product and graph-theoretic methods where appropriate. It presents a series of fundamental results: invertibility, observability, detectability, reversiblity, etc., with applications to systems biology.
Academic researchers with backgrounds in applied mathematics, engineering or computer science and practising engineers working with discrete-time and discrete-space systems will find this book a helpful source of new understanding for this increasingly important class of systems. The basic results to be found within are of fundamental importance for further study of related problems such as automated synthesis and safety control in cyber-physical systems using formal methods.
Contents
Introduction.- Preliminaries.- Introduction to Different Types of Discrete-Time and Discrete-Space Dynamical Systems.- Invertibility and Nonsingularity of Boolean Control Networks.- Observability of Boolean Control Networks.- Detectability of Boolean Control Networks.- Observability and Detectability of Large-Scale Boolean Control Networks.- Observability of Nondeterministic Finite-Transition Systems.- Detectability of Nondeterministic Finite-Transition Systems.- Detectability of Finite-State Automata.- Detectability of Labelled Petri Nets.- Generalized Reversibility of Topological Dynamical Systems and Cellular Automata.- Generalized Reversibility of Variant Cellular Automata.- Solutions.- Index.
