## Turing’s Connectionism: An Investigation of Neural Network ArchitecturesAlan Mathison Turing (1912-1954) was the first to carry out substantial re search in the field now known as Artificial Intelligence (AI). He was thinking about machine intelligence at least as early as 1941 and during the war cir culated a typewritten paper on machine intelligence among his colleagues at the Government Code and Cypher School (GC & CS), Bletchley Park. Now lost, this was undoubtedly the earliest paper in the field of AI. It probably concerned machine learning and heuristic problem-solving; both were topics that Turing discussed extensively during the war years at GC & CS, as was mechanical chess [121]. In 1945, the war in Europe over, Turing was recruited by the National Physical Laboratory (NPL)! in London, his brief to design and develop an electronic stored-program digital computer-a concrete form of the universal Turing machine of 1936 [185]. Turing's technical report "Proposed Electronic 2 Calculator" , dating from the end of 1945 and containing his design for the Automatic Computing Engine (ACE), was the first relatively complete spec ification of an electronic stored-program digital computer [193,197]. (The document "First Draft of a Report on the EDVAC", produced by John von Neumann and the Moore School group at the University of Pennsylvania in May 1945, contained little engineering detail, in particular concerning elec tronic hardware [202]. |

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### Contents

1 Introduction | 1 |

12 Alan Mathison Turing | 4 |

13 Connectionism and Artificial Neural Networks | 6 |

14 Historical Context and Related Work | 10 |

15 Organization of the Book | 13 |

16 Book WebSite | 15 |

2 Intelligent Machinery | 17 |

21 Machines | 18 |

38 Hardware Implementation | 77 |

4 Organizing Unorganized Machines | 83 |

41 Evolutionary Algorithms | 84 |

42 Evolutionary Artificial Neural Networks | 86 |

422 Encoding Techniques | 87 |

423 Atype Network Encoding | 88 |

424 Btype Network Encoding | 90 |

426 LSystem Encoding | 93 |

212 Turing Machines | 19 |

213 Universal Turing Machines | 20 |

214 Practical Computing Machines | 21 |

215 Ptype Machines | 22 |

221 Fundamentals and Definitions | 23 |

222 Atype Unorganized Machines | 26 |

224 Turings Education of Machinery | 28 |

225 BItype Unorganized Machines | 29 |

23 Formalization and Analysis of Unorganized Machines | 31 |

231 Formalization of Atype Networks | 32 |

232 Formalization of Btype Links | 37 |

233 Formalization of Btype Networks | 41 |

234 Formalization of BItype Links | 42 |

235 Formalization of BItype Networks | 44 |

236 The Btype Pitfall | 45 |

24 New Unorganized Machines | 48 |

242 TBtype Unorganized Machines | 50 |

243 TBItype Unorganized Machines | 51 |

244 BStype Unorganized Machines | 52 |

245 BI1type Link | 54 |

25 Simulation of TBItype Machines with MATLAB | 55 |

3 Synthesis of Logical Functions and Digital Systems with Turing Networks | 63 |

32 Synthesis of Logical Functions with Atype Networks | 64 |

33 Synthesis of Logical Functions with TBtype Networks | 67 |

35 DelayUnit | 70 |

36 ShiftRegister | 72 |

37 How to Design Complex Systems | 74 |

Evolve Networks that Regenerate Bitstreams | 97 |

44 Signal Processing in Turing Networks | 101 |

45 Pattern Classification | 106 |

Pattern Classification with Genetic Algorithms | 109 |

47 A Learning Algorithm for Turing Networks | 117 |

5 Network Properties and Characteristics | 121 |

52 Computational Power | 123 |

53 State Machines | 125 |

54 Threshold Logic | 127 |

55 Dynamical Systems and the StateSpace Model | 131 |

56 Random Boolean Networks | 133 |

57 Attractors | 135 |

58 Network Stability and Activity | 138 |

581 Activity in Atype Networks | 142 |

582 Activity in BStype Networks | 144 |

583 Activities in TBtype and TBItype Networks | 147 |

59 Chaos Bifurcation and SelfOrganized Criticality | 148 |

510 Topological Evolution and SelfOrganization | 157 |

Computing Beyond the Turing Limit with Turings Neural Networks? | 163 |

6 Epilogue | 169 |

Useful WebSites | 171 |

List of Figures | 173 |

List of Tables | 181 |

List of Examples Theorems Definitions Propositions and Corollaries | 183 |

187 | |

197 | |

### Common terms and phrases

100-node A-type network 5x5 dot A-type machine A-type network A-type node A-type unorganized machine artificial neural networks attractors B-type link behaviour binary bitstream boolean networks brain Church-Turing thesis clock cycles complex configuration connectionism connectionist Copeland and Proudfoot CP-type Definition delay described disabled dynamical systems enabled connections encoding evolution evolutionary algorithm example finite flip-flop function realized genetic algorithm hardware Hypercomputation implementation incoming links initial node values input nodes inputs and outputs interconnection switches inverter L-system links per node logical functions MATLAB matrix McCulloch-Pitts monostable NAND gate network architecture network genome network nodes network output Network steps neurons output activity output nodes parameters possible presented problem Proposition random boolean networks randomly regenerated Section self-organizing shift-register shown in Figure shows signal simulated stable std_logic Supervised learning tape TBI-type network threshold elements Turing networks Turing neural networks Turing's neural networks Two-input Typical activities unit universal Turing machine vector VHDL weights