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Preliminaries

  • Kuize ZhangEmail author
  • Lijun Zhang
  • Lihua Xie
Chapter
Part of the Communications and Control Engineering book series (CCE)

Abstract

In this chapter, we introduce basic theoretical tools used throughout the book, that is, graph theory, the semitensor product of matrices, finite automata, and topology. As in the reading flow shown in Fig. 0.1, topology is used to study invertibility (Sect.  3.2) of Boolean control networks and generalized reversibility (Chap.  11) of cellular automata; graph theory is used to characterize nonsingularity (Sect.  3.3) of Boolean control networks, observability (Sect.  4.2) and detectability (Sect.  5.2) of Boolean control networks and large-scale Boolean control networks (Chap.  6); the semitensor product of matrices is used to give an intuitive matrix representation for Boolean control networks (Chap.  3); the theory of finite automata is used to investigate observability (Sect.  4.2) and detectability (Sect.  5.2) of Boolean control networks, observability (Chap.  7) and detectability (Chap.  8) of nondeterministic finite-transition systems, and detectability of finite-state automata (Chap.  9); some existing theoretical results in labeled Petri nets are used to study detectability of labeled Petri nets (Chap.  10).

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.School of Electrical Engineering and Computer ScienceKTH Royal Institute of TechnologyStockholmSweden
  2. 2.School of Marine Science and TechnologyNorthwestern Polytechnical UniversityXi’anChina
  3. 3.School of Electrical and Electronic EngineeringNanyang Technological UniversitySingaporeSingapore

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