A New Kind of Science

Early in the 1980s Stephen Wolfram began to work in earnest upon cellular automata. These are a class of computer model which may be visualized as a set of memory locations, each containing one bit. These bits are updated in a succession of time steps. In each step, the new value of each bit depends upon the values of neighboring bits. Wolfram particularly studied the class of automata in which all the bits are arranged upon a line, and each bit is updated using the very same functional dependence upon the bits at that site and its two nearest neighbors. There are 256 different automata of this type. Wolfram made it his business to study systematically all of these different automata, using extensive computer simulations, and to think about and generalize from what he thereby uncovered. A New Kind of Science, written and published by Stephen Wolfram, is the outcome of these, and related, studies.

[1]  John Cocke,et al.  Universality of Tag Systems with P = 2 , 1964, JACM.

[2]  R. Feynman.  The Character of Physical Law , 1965 .

[3]  Leslie G. Valiant,et al.  The Complexity of Computing the Permanent , 1979, Theor. Comput. Sci..

[4]  Leonid A. Levin,et al.  Average Case Complete Problems , 1986, SIAM J. Comput..

[5]  Heiner Marxen,et al.  Attacking the Busy Beaver 5 , 1990, Bull. EATCS.

[6]  A. Shimony,et al.  Bell’s theorem without inequalities , 1990 .

[7]  John Watrous,et al.  On one-dimensional quantum cellular automata , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[8]  David G. Mitchell,et al.  Finding hard instances of the satisfiability problem: A survey , 1996, Satisfiability Problem: Theory and Applications.

[9]  Cynthia Dwork,et al.  A public-key cryptosystem with worst-case/average-case equivalence , 1997, STOC '97.

[10]  L. Smolin,et al.  Causal evolution of spin networks , 1997 .

[11]  Umesh V. Vazirani,et al.  Quantum Complexity Theory , 1997, SIAM J. Comput..

[12]  T. Nowotny,et al.  Dimension theory of graphs and networks , 1997, hep-th/9707082.

[13]  Leonid A. Levin,et al.  A Pseudorandom Generator from any One-way Function , 1999, SIAM J. Comput..

[14]  G. Hooft.  Quantum gravity as a dissipative deterministic system , 1999, gr-qc/9903084.

[15]  R. Sorkin,et al.  Classical sequential growth dynamics for causal sets , 1999, gr-qc/9904062.

[16]  L. Crane.  A New Approach to the Geometrization of Matter , 2001, gr-qc/0110060.

[17]  Christopher Umans.  The Minimum Equivalent DNF Problem and Shortest Implicants , 2001, J. Comput. Syst. Sci..

[18]  N. Gisin,et al.  Quantum correlations with spacelike separated beam splitters in motion: experimental test of multisimultaneity. , 2002, Physical review letters.

[19]  R. Bousso.  The Holographic principle , 2002, hep-th/0203101.

[20]  James Park,et al.  A New Kind of Science , 2003, Artificial Life.

[21]  Yaoyun Shi.  Both Toffoli and controlled-NOT need little help to do universal quantum computing , 2003, Quantum Inf. Comput..