Computational Complexity in Physics

There are many definitions of the word “complexity.” These fall into three main categories: Information and thermodynamic entropy, as in Shannon and Gibbs, with extensions by Crutchfield and others Minimum description length, as in Kolmogorov and Chaitin, and physical versions of this, as in Lloyd, Pagels and Gell-Mann Computational complexity.

[1]  Mats G. Nordahl,et al.  Universal Computation in Simple One-Dimensional Cellular Automata , 1990, Complex Syst..

[2]  Jonathan Machta The computational complexity of pattern formation , 1993 .

[3]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[4]  Cristopher Moore,et al.  Internal Diffusion-Limited Aggregation: Parallel Algorithms and Complexity , 1999, cond-mat/9909233.

[5]  Cristopher Moore,et al.  The phase transition in 1-in-k SAT and NAE 3-SAT , 2001, SODA '01.

[6]  J. Machta,et al.  The computational complexity of generating random fractals , 1996 .

[7]  Cristopher Moore,et al.  Predicting nonlinear cellular automata quickly by decomposing them into linear ones , 1997, patt-sol/9701008.

[8]  Olivier Dubois,et al.  Typical random 3-SAT formulae and the satisfiability threshold , 2000, SODA '00.

[9]  Cristopher Moore,et al.  Quasilinear cellular automata , 1997, adap-org/9701001.

[10]  F. Barahona On the computational complexity of Ising spin glass models , 1982 .

[11]  H. James Hoover,et al.  Limits to Parallel Computation: P-Completeness Theory , 1995 .

[12]  Cristopher Moore,et al.  Height Representation, Critical Exponents, and Ergodicity in the Four-State Triangular Potts Antiferromagnet , 1999, cond-mat/9902295.

[13]  P. Odifreddi Classical recursion theory , 1989 .

[14]  Martin Nilsson,et al.  The Computational Complexity of Sandpiles , 1999 .

[15]  Cristopher Moore Majority-Vote Cellular Automata, Ising Dynamics, and P-Completeness , 1997 .

[16]  Dimitris Achlioptas,et al.  Optimal myopic algorithms for random 3-SAT , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[17]  Rémi Monasson,et al.  Determining computational complexity from characteristic ‘phase transitions’ , 1999, Nature.