Irreducibility and Computational Equivalence

I. Mechanisms in Programs and Nature

1. Cellular Automata: Models of the Physical World
Herbert W. Franke

2. On the Necessity of Complexity
Joost J. Joosten

3. A Lyapunov View on the Stability of Two-State Cellular Automata
Jan M. Baetens, Bernard Baets

II. Systems Based on Numbers and Simple Programs

4. Cellular Automata and Hyperbolic Spaces
Maurice Margenstern

5. Symmetry and Complexity of Cellular Automata: Towards an Analytical Theory of Dynamical System
Klaus Mainzer, Carl Linde-Akademie

6. A New Kind of Science: Ten Years Later
David H. Bailey

III. Mechanisms in Biology, Social Systems and Technology

7. More Complex Complexity: Exploring the Nature of Computational Irreducibility across Physical, Biological, and Human Social Systems
Brian Beckage, Stuart Kauffman, Louis J. Gross, Asim Zia, Christopher Koliba

8. A New Kind of Finance
Philip Z. Maymin

9. The Relevance of Computation
Irreducibility as Computation
Universality in Economics
K. Vela Velupillai

10. Computational Technosphere and Cellular Engineering
Mark Burgin

IV. Fundamental Physics

11. The Principle of a Finite Density of Information
Pablo Arrighi, Gilles Dowek

12. Do Particles Evolve?
Tommaso Bolognesi

13. Artificial Cosmogenesis: A New Kind of Cosmology
Clément Vidal

V. The Behavior of Systems and the Notion of Computation

14. An Incompleteness Theorem for the Natural World
Rudy Rucker

15. Pervasiveness of Universalities of Cellular Automata: Fascinating Life-Like Behaviours
Emmanuel Sapin

16. A Spectral Portrait of the Elementary Cellular Automata Rule Space
Eurico L. P. Ruivo, Pedro P. B. Oliveira

17. Wolfram’s Classification and Computation in Cellular Automata Classes III and IV
Genaro J. Martínez, Juan C. Seck-Tuoh-Mora, Hector Zenil

VI. Irreducibility and Computational Equivalence

18. Exploring Wolfram’s Notion of Computational Irreducibility with a Two-Dimensional Cellular Automaton
Drew Reisinger, Taylor Martin, Mason Blankenship, Christopher Harrison, Jesse Squires, Anthony Beavers

19. Unpredictability and Computational Irreducibility
Hervé Zwirn, Jean-Paul Delahaye

20. Computational Equivalence and Classical Recursion Theory
Klaus Sutner

VII. Reflections and Philosophical Implications

21. Wolfram and the Computing Nature
Gordana Dodig-Crnkovic

22. A New Kind of Philosophy: Manifesto for a Digital Ontology
Jacopo Tagliabue

23. Free Will and A
New
Kind
of
Science

Selmer Bringsjord

24. Erratum: Symmetry and Complexity of Cellular Automata: Towards an Analytical Theory of Dynamical System
Klaus Mainzer

Keywords: Engineering, Complexity, Computational Intelligence, Artificial Intelligence (incl. Robotics)