Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

Planning Algorithms: Introductory Material

Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new andpromising methods for the numerical solution of nonlinear partial differential equations. The bookprovides an introduction for graduate students and researchers. Working knowledge of calculus isrequired and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellularautomata are outlined in Chapter 2. The properties of various LGCA and special coding techniquesare discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessarytheoretical background for LGCA and LBM. The properties of lattice Boltzmann models and amethod for their construction are presented in Chapter 5.

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Lattice-Gas Cellular Automata and Lattice Boltzmann Models

Lattice-Gas Cellular Automata and Lattice Boltzmann Models: An Introduction

Every organisation from the scale of whole countries down to small companies has a list of system developments which have ended in various forms of disaster. The nature of the failures varies but typical examples are: cost overruns; timescale overruns and sometimes, loss of life. The post-mortems to these systems reveal a wide range of reasons all the way from hardware failures, through software errors right to major system level mistakes. More importantly a large number of these systems share one attribute: complexity. This paper presents a fresh look at the nature of complexity in the building of computer based systems.

http://ieeexplore.ieee.org/iel3/4458/12639/00581896.pdf

Complex systems

https://www.ibisc.univ-evry.fr/~hutzler/Cours/IMBI_MPS/Kari05.pdf

Theory of cellular automata: a survey

Classifying circular cellular automata

Suppose each of the squares of an n x n chessboard is equipped with an indicator light and a button. If the button of a square is pressed, the light of that square will change from off to on and vice versa; the same happens to the lights of all the edge-adjacent squares. Initially all lights are off. Now, consider the following question: is it possible to press a sequence of buttons in such a way that in the end all lights are on? We will refer to this problem as the All-Ones Problem. A moment 's reflection will show that pressing a button twice has the same effect as not pressing it at all. Thus a solution to our problem can be described by a subset of all squares (namely a set of squares whose buttons when pressed in an arbitrary order will render all lights on) rather than a sequence. In fact a set X of squares is a solution to the All-Ones Problem if and only if for every square s the number of squares in X adjacent to or equal to s is odd. Consequently, we will call such a set an odd-parity cover. Trial and error in conjunction with a pad of graph paper will readily produce solutions for n ~ 4. A little more experimentation shows that an odd-parity cover shou ld one exist--is difficult to construct even for n = 5 o r 6 . The brute-force approach to the problem, namely exhaustive search over all subsets of {1 . . . . n} x {1 . . . . n}, presents 2 n2 candidates, and the search becomes infeasible for moderate values of n even with the help of a computer. A less brute-force method would be to try to solve the system terpreted as a matrix over GF(2)) and 1 is the vector with all components equal to 1. This method, which involves n 2 equations, again becomes unwieldy for small values of n. For a similar approach to a game related to the All-Ones Problem, see [3]. In any case, Figure 1 shows odd-parity covers for n = 4, 5, 8. Several questions come to mind. For which n does a solution to the All-Ones Problem exist? More generally, how many odd-parity covers are there for an n x n board? What happens if the adjacency condition is changed--say , to an octal array (where a cell in the center has eight neighbors)? Can one replace an n x n rectangular grid by some other arrangement of sites and still obtain a solution? To answer some of these questions, we first rephrase the problem in terms of cellular automata.

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Linear cellular automata and the garden-of-eden

De Bruij n graphs provide a convenient way to describe configura tions of linear cellular automata (CAs). Using t hese gra phs, we give a simple quadra t ic t ime algorithm to det ermine whet her a linear CA is reversible. Similarly, one can decide in quadrat ic time whet her t he global map of th e auto mato n is surjective. We also show tha t every recursive configuration that has a predecessor on a linear CA already has a recursive pr edecessor. By contradist inction, it is in genera l impossible to comput e such a predecessor effect ively.

Klaus Sutner

Papers

Classifying circular cellular automata

Linear cellular automata and the garden-of-eden

De Bruijn Graph s and Linear Cellular Automata

On σ-automata

On the Computational Complexity of Finite Cellular Automata