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Building a Universal Machine

A Hands-on Introduction to Computability

Tomas Tulka

From the foundations of computing to the construction of electronic devices, this book attempts to build an easy-to-cross bridge between theory and practice, model and reality, thought and object.

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About

About

About the Book

From the foundations of computing to the construction of electronic devices, this book attempts to build an easy-to-cross bridge between theory and practice, model and reality, thought and object.

A comprehensive, step-by-step guide to understanding how computers work, tracing their evolution from ancient logic to modern electronic circuits. It explores key theoretical concepts—such as finite automata, formal languages, Turing machines, universal computation, register machines, recursive functions, lambda calculus, tag systems, cellular automata, and hypercomputation—as well as the development of mechanical and electronic computers.

Written in a friendly, informal style, it emphasizes the big picture and the joy of exploration rather than dry mathematical formalisms. The hands-on approach ensures that readers grasp the fundamentals as they progressively build a universal computer in JavaScript using only the knowledge they've learned along the way.

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Computers and ProgrammingComputing HistoryComputer Science

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Author

About the Author

Tomas Tulka

is keen on building small machines

Contents

Table of Contents

About the Book

  1. Welcome to the Machine

In Pursuit of Mechanical Thought

  1. Logic
  2. Hilbert’s Dream
  3. Incompleteness
  4. Entscheidungsproblem
  5. Church–Turing Thesis
  6. Timeline

Everything Is a Number

  1. Numeral Systems
  2. Sets
  3. Numbers
  4. Abstract Machines

Simple Machines

  1. Finite Automata
  2. Nondeterministic Finite Automata
  3. Regular Languages and Expressions
  4. Pushdown Automata
  5. Nondeterministic Pushdown Automata
  6. Probabilistic Automata
  7. Context-Free Languages
  8. Linear Bounded Automata
  9. Context-Sensitive Languages

Universal Machines

  1. Turing Machines
  2. Decidable Languages
  3. Subroutines
  4. Multitape
  5. Fixed-End Tape
  6. Nondeterministic Machines
  7. Restricted Alphabets
  8. Universal Turing Machines
  9. Input Encoding
  10. Virtual Tapes
  11. Design
  12. Implementation
  13. Testing
  14. Programming
  15. Rrr
  16. All the Way Down
  17. The Halting Problem
  18. Semi-Decidable Languages

Number Machines

  1. Register Machines
  2. Counter Machines
  3. Random-Access Machines
  4. Stored-Program Machines
  5. Universal Register Machine
  6. Recursive Functions
  7. Primitive recursion
  8. Partial Recursion
  9. Universal Recursive Function
  10. Simulating Recursive Functions

Programming Machines

  1. Turing Completeness
  2. Structured Programming

Small Machines

  1. Minimal-State Turing Machines
  2. Wolfram 2,3
  3. Lambda Calculus
  4. Non-Halting Lambda Functions
  5. Syntactic Sugar
  6. Numbers
  7. Functional Programming
  8. Combinatory Logic
  9. Tag Systems
  10. Universal Tag Systems
  11. Cyclic Tag Systems
  12. Cellular Automata
  13. The Game of Life
  14. Universal Cells
  15. Rules
  16. One-Instruction Set Computers

Hyper Machines

  1. Quantum Computers
  2. Super-Recursive Algorithms
  3. Oracles
  4. Inductive Turing Machines
  5. Exotic Machines
  6. Actual Machines

Mechanical Machines

  1. Ancient Devices
  2. Medieval Inventions
  3. First Reckoners
  4. Pascaline
  5. Leibniz Calculator
  6. Jacquard Loom
  7. Early Computers
  8. Analytical Engine
  9. Z3
  10. Mark I
  11. ENIAC
  12. EDVAC

Logic Machines

  1. Logic Gates
  2. NOT Gate
  3. AND Gate
  4. OR Gates
  5. XOR Gate
  6. NOR Gate
  7. NAND Gate
  8. Logic Circuits
  9. Arithmetics
  10. Multiplexers
  11. Storages

Electronic Machines

  1. Integrated Circuits
  2. Transistors

Computer Machines

  1. Clock
  2. Cache
  3. Memory
  4. Universal Computer
  5. Processor
  6. Goodbye, Machine

Mind Machines

  1. Universality
  2. Computing the Universe
  3. Machines Like Us
  4. In Summary

Appendix

  1. Examples of Turing Machines
  2. Copier
  3. Palindromes
  4. Hello World
  5. Universal Turing Machine
  6. Structured Universal Machine
  7. Structured Universal Machine (Extended)
  8. Universal Minsky Machine
  9. Universal Recursive Function in JavaScript
  10. Universal Tag System
  11. Lambda Calculus Generic Recursion

References

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