| Preface | p. V |
| What is a Sequential Dynamical System? | p. 1 |
| Sequential Dynamical Systems: A First Look | p. 1 |
| Motivation | p. 4 |
| Application Paradigms | p. 7 |
| TRANSIMS | p. 7 |
| Task Scheduling and Transport Computations | p. 13 |
| SDS: Characteristics and Research Questions | p. 16 |
| Update Order Dependencies | p. 16 |
| Phase-Space Structure | p. 17 |
| Computational and Algorithmic Aspects | p. 18 |
| Summary | p. 20 |
| Problems | p. 20 |
| Answers to Problems | p. 22 |
| A Comparative Study | p. 23 |
| Cellular Automata | p. 23 |
| Background | p. 23 |
| Structure of Cellular Automata | p. 24 |
| Elementary CA Rules | p. 27 |
| Random Boolean Networks | p. 33 |
| Finite-State Machines (FSMs) | p. 34 |
| Problems | p. 35 |
| Answers to Problems | p. 37 |
| Graphs, Groups, and Dynamical Systems | p. 39 |
| Graphs | p. 39 |
| Simple Graphs and Combinatorial Graphs | p. 41 |
| The Adjacency Matrix of a Graph | p. 44 |
| Acyclic Orientations | p. 46 |
| The Update Graph | p. 47 |
| Graphs, Permutations, and Acyclic Orientations | p. 48 |
| Group Actions | p. 50 |
| Groups Acting on Graphs | p. 51 |
| Groups Acting on Acyclic Orientations | p. 52 |
| Dynamical Systems | p. 56 |
| Classical Continuous Dynamical Systems | p. 57 |
| Classical Discrete Dynamical Systems | p. 59 |
| Linear and Nonlinear Systems | p. 61 |
| Problems | p. 63 |
| Answers to Problems | p. 66 |
| Sequential Dynamical Systems over Permutations | p. 69 |
| Definitions and Terminology | p. 69 |
| States, Vertex Functions, and Local Maps | p. 69 |
| Sequential Dynamical Systems | p. 71 |
| The Phase Space of an SDS | p. 73 |
| SDS Analysis - A Note on Approach and Comments | p. 76 |
| Basic Properties | p. 77 |
| Decomposition of SDS | p. 77 |
| Fixed Points | p. 78 |
| Reversible Dynamics and Livertibility | p. 80 |
| Invertible SDS with Symmetric Functions over Finite Fields | p. 84 |
| Equivalence | p. 88 |
| Functional Equivalence of SDS | p. 90 |
| Computing Equivalence Classes | p. 91 |
| Dynamical Equivalence | p. 93 |
| Enumeration of Dynamically Nonequivalent SDS | p. 97 |
| SDS Morphisms and Reductions | p. 103 |
| Covering Maps | p. 104 |
| Properties of Covering Maps | p. 104 |
| Reduction of SDS | p. 105 |
| Dynamical Equivalence Revisited | p. 109 |
| Construction of Covering Maps | p. 110 |
| Covering Maps over Q[Characters not reproducible] | p. 111 |
| Covering Maps over Circ[subscript n] | p. 119 |
| Problems | p. 121 |
| Answers to Problems | p. 122 |
| Phase-Space Structure of SDS and Special Systems | p. 129 |
| Fixed Points for SDS over Circ[subscript n] and Circ[subscript n] | p. 129 |
| Fixed-Point Computations for General Graphs | p. 137 |
| Threshold SDS | p. 139 |
| SDS over Special Graph Classes | p. 140 |
| SDS over the Complete Graph | p. 141 |
| SDS over the Circle Graph | p. 143 |
| SDS over the Line Graph | p. 145 |
| SDS over the Star Graph | p. 146 |
| SDS Induced by Special Function Classes | p. 146 |
| SDS Induced by (nor[subscript k])[subscript k] (nan[subscript k])[subscript k] | p. 147 |
| SDS Induced by (nor[subscript k] + nand[subscript k])[subscript k] | p. 154 |
| Problems | p. 158 |
| Answers to Problems | p. 160 |
| Graphs, Groups, and SDS | p. 165 |
| SDS with Order-Independent Periodic Points | p. 165 |
| Preliminaries | p. 166 |
| The Group G(Y, F[subscript Y]) | p. 167 |
| The Class of w-Independent SDS | p. 171 |
| The Class of w-Independent SDS over Circ[subscript n] | p. 174 |
| The Groups G(Circ[subscript 4], F[subscript Circ4] | p. 176 |
| A Presentation of S[subscript 35] | p. 178 |
| Problems | p. 179 |
| Answers to Problems | p. 182 |
| Combinatorics of Sequential Dynamical Systems over Words | p. 185 |
| Combinatorics of SDS over Words | p. 187 |
| Dependency Graphs | p. 187 |
| Automorphisms | p. 189 |
| Words | p. 192 |
| Acyclic Orientations | p. 193 |
| The Mapping O[subscript Y] | p. 195 |
| A Normal Form Result | p. 197 |
| The Bijection | p. 198 |
| Combinatorics of SDS over Words | p. 199 |
| Generalized Equivalences | p. 199 |
| The Bijection (P1) | p. 201 |
| Equivalence (P2) | p. 204 |
| Phase-Space Relations | p. 206 |
| Problems | p. 209 |
| Answers to Problems | p. 210 |
| Outlook | p. 213 |
| Stochastic SDS | p. 213 |
| Random Update Order | p. 214 |
| SDS over Random Graphs | p. 217 |
| Gene-Regulatory Networks | p. 217 |
| Introduction | p. 217 |
| The Tryptophan-Operon | p. 218 |
| Evolutionary Optimization of SDS-Schedules | p. 220 |
| Neutral Networks and Phenotypes of RNA and SDS | p. 220 |
| Distances | p. 223 |
| A Replication-Deletion Scheme | p. 226 |
| Evolution of SDS-Schedules | p. 227 |
| Pseudo-Codes | p. 228 |
| Discrete Derivatives | p. 229 |
| Real-Valued and Continuous SDS | p. 231 |
| L-Local SDS | p. 233 |
| Routing | p. 234 |
| Weights | p. 234 |
| Protocols as Local Maps | p. 235 |
| References | p. 237 |
| Index | p. 245 |
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