Dynamical Recognizers: Real-time Language Recognition by Analog Computers (Extended Abstract)

We consider a model of analog computation which performs language recognition in real time. We encode an input word as a point in ℝ d by composing iterated maps, and then apply inequalities to the resulting point to test for membership in the language.

[1]  Klaus Meer Real Number Models under Various Sets of Operations , 1993, J. Complex..

[2]  Hava T. Siegelmann,et al.  Analog computation via neural networks , 1993, [1993] The 2nd Israel Symposium on Theory and Computing Systems.

[3]  Paul W. Goldberg,et al.  Bounding the Vapnik-Chervonenkis Dimension of Concept Classes Parameterized by Real Numbers , 1993, COLT '93.

[4]  Arnold L. Rosenberg,et al.  Real-Time Definable Languages , 1967, JACM.

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

[6]  S. Smale,et al.  On a theory of computation and complexity over the real numbers; np-completeness , 1989 .

[7]  H. Warren Lower bounds for approximation by nonlinear manifolds , 1968 .

[8]  Pascal Koiran A Weak Version of the Blum, Shub, and Smale Model , 1997, J. Comput. Syst. Sci..

[9]  Cristopher Moore,et al.  Dynamical Recognizers: Real-Time Language Recognition by Analog Computers , 1998, Theor. Comput. Sci..

[10]  Jordan B. Pollack,et al.  The induction of dynamical recognizers , 1991, Machine Learning.

[11]  Pascal Koiran Computing over the Reals with Addition and Order , 1994, Theor. Comput. Sci..

[12]  Jeffrey L. Elman,et al.  Language as a dynamical system , 1996 .

[13]  Dima Grigoriev,et al.  On the Power of Real Turing Machines Over Binary Inputs , 1997, SIAM J. Comput..

[14]  T. Gelder,et al.  Mind as Motion: Explorations in the Dynamics of Cognition , 1995 .

[15]  Klaus Meer,et al.  Descriptive complexity theory over the real numbers , 1995, STOC '95.

[16]  C. Lee Giles,et al.  Using Prior Knowledge in a {NNPDA} to Learn Context-Free Languages , 1992, NIPS.

[17]  David Haussler,et al.  Learnability and the Vapnik-Chervonenkis dimension , 1989, JACM.