Discrete-Time and Discrete-Space Dynamical Systems

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; andcellular 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. Front Matter ....Pages i-xiv Front Matter ....Pages 1-1 Preliminaries (Kuize Zhang, Lijun Zhang, Lihua Xie)....Pages 3-33 Different Types of Discrete-Time and Discrete-Space Dynamical Systems (Kuize Zhang, Lijun Zhang, Lihua Xie)....Pages 35-56 Front Matter ....Pages 57-57 Invertibility and Nonsingularity of Boolean Control Networks (Kuize Zhang, Lijun Zhang, Lihua Xie)....Pages 59-86 Observability of Boolean Control Networks (Kuize Zhang, Lijun Zhang, Lihua Xie)....Pages 87-104 Detectability of Boolean Control Networks (Kuize Zhang, Lijun Zhang, Lihua Xie)....Pages 105-115 Observability and Detectability of Large-Scale Boolean Control Networks (Kuize Zhang, Lijun Zhang, Lihua Xie)....Pages 117-142 Front Matter ....Pages 143-143 Observability of Nondeterministic Finite-Transition Systems (Kuize Zhang, Lijun Zhang, Lihua Xie)....Pages 145-163 Detectability of Nondeterministic Finite-Transition Systems (Kuize Zhang, Lijun Zhang, Lihua Xie)....Pages 165-175 Front Matter ....Pages 177-177 Detectability of Finite-State Automata (Kuize Zhang, Lijun Zhang, Lihua Xie)....Pages 179-192 Front Matter ....Pages 193-193 Detectability of Labeled Petri Nets (Kuize Zhang, Lijun Zhang, Lihua Xie)....Pages 195-209 Front Matter ....Pages 211-211 Generalized Reversibility of Cellular Automata (Kuize Zhang, Lijun Zhang, Lihua Xie)....Pages 213-220 Back Matter ....Pages 221-222