Reconstructing Language Hierarchies

Within an assumed language class optimal models can be estimated using Gibb-sian statistical mechanics. But how are model classes themselves related? We consider the problem of moving from less to more computationally capable classes in the search for finite descriptions of unpredictable data series.

[1]  Roland Fischer Sofic systems and graphs , 1975 .

[2]  James P. Crutchfield,et al.  Equations of Motion from a Data Series , 1987, Complex Syst..

[3]  David A. Huffman,et al.  The synthesis of sequential switching circuits , 1954 .

[4]  S. Wolfram Computation theory of cellular automata , 1984 .

[5]  Richard E. Blahut,et al.  Principles and practice of information theory , 1987 .

[6]  N. Packard,et al.  Symbolic dynamics of noisy chaos , 1983 .

[7]  Gregory J. Chaitin,et al.  On the Length of Programs for Computing Finite Binary Sequences , 1966, JACM.

[8]  D. Dennett The Intentional Stance. , 1987 .

[9]  James P. Crutchfield,et al.  Noise Scaling of Symbolic Dynamics Entropies , 1982 .

[10]  Young,et al.  Inferring statistical complexity. , 1989, Physical review letters.

[11]  A. Rényi On the dimension and entropy of probability distributions , 1959 .

[12]  J. Rissanen Stochastic Complexity and Modeling , 1986 .

[13]  James P. Crutchfield,et al.  Inferring the Dynamic, Quantifying Physical Complexity , 1989 .

[14]  P. Grassberger Toward a quantitative theory of self-generated complexity , 1986 .

[15]  Claude E. Shannon,et al.  The Mathematical Theory of Communication , 1950 .

[16]  Michael Doob,et al.  Spectra of graphs , 1980 .

[17]  J. Crutchfield Information and Its Metric , 1990 .

[18]  Carl H. Smith,et al.  Inductive Inference: Theory and Methods , 1983, CSUR.

[19]  Ray J. Solomonoff,et al.  A Formal Theory of Inductive Inference. Part II , 1964, Inf. Control..

[20]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[21]  E. T. Jaynes,et al.  Where do we Stand on Maximum Entropy , 1979 .

[22]  Neal B. Abraham,et al.  Measures of Complexity and Chaos , 1990 .

[23]  N. Packard,et al.  Symbolic dynamics of one-dimensional maps: Entropies, finite precision, and noise , 1982 .

[24]  Noam Chomsky,et al.  Three models for the description of language , 1956, IRE Trans. Inf. Theory.

[25]  Hermann Haken,et al.  Evolution of Order and Chaos , 1982 .

[26]  John G. Kemeny,et al.  The Use of Simplicity in Induction , 1953 .

[27]  G. Toulouse,et al.  Ultrametricity for physicists , 1986 .