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By Bruce E. Nevin (Ed.), Stephen M. Johnson (Ed.)

Zellig Harris had a profound effect in formal structures and utilized arithmetic, in demonstrations of the computability of language, and in informatics. quantity 2 starts off with a observation via André Lentin on Harris's grounding in constructivist, intuitionist arithmetic, drawing a parallel among Harris's relevant insights and people of Gödel and others that have been of like import within the foundations of arithmetic. An Read more...

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Additional resources for The Legacy of Zellig Harris: Language and Information into the 21st Century, Vol. 2: Mathematics and Computability of Language

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Dempster, A. , N. M. Laird, & D. B. Rubin. 1977. 1:ƒƒ1–38. Freund, Y. 1998. ’’ Proceedings of the Eleventh Annual Conference on Computational Learning Theory, 247–258. ACM. Freund, Y. & R. Schapire. 1997. 1:ƒƒ119–139. Gale, W. , K. W. Church, & D. Yarowsky. 1992. ’’ Proceedings of the 4th DARPA Speech and Natural Language Workshop, 233–237). San Francisco, California: Morgan Kaufmann. Good, I. J. 1953. 3/4:ƒƒ237–264. Harris, Z. S. 1951. Structural Linguistics. Chicago, Illinois: University of Chicago Press.

Harris, Z. S. 1991. A Theory of Language and Information: A mathematical approach. New York: Clarendon Press. Horning, J. J. 1969. A Study of Grammatical Inference. PhD dissertation, Stanford University. Jelinek, F. & R. L. Mercer. 1980. ’’ Proceedings of the Workshop on Pattern Recognition in Practice. Amsterdam: North Holland. Katz, S. M. 1987. 3:ƒƒ400–401. Kearns, M. J. & L. G. Valiant. 1994. 1:ƒƒ67–95. Lambek, J. 1958. ’’ American Mathematical Monthly 65:ƒƒ154–170. Littlestone, N. & M. Warmuth.

Wn ) by n p (w1 Kwn ) = p (w1)∏ p (wi | wi −1). i=2 Using this estimate for the probability of a string and an aggregate model with C=16 trained on newspaper text using the expectation-maximization (EM) method (Dempster et al. 1977), we find that p (Colorless green ideas sleep furiously) ≈ 2 × 105 p (Furiously sleep ideas green colorless) Formal grammar and information theory Thus, a suitably constrained statistical model, even a very simple one, can meet Chomsky’s particular challenge. A plausible and well-defined model of the statistical dependencies among the hidden variables is however not in general sufficient, since the problem of setting the corresponding conditional probabilities from observable linguistic material is in most cases computationally intractable (Abe & Warmuth 1992).

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