1. Basic work on this phenomenon in neural network models, and critiques, include D. E. Rumelhart and J. L. McClelland, in Parallel Distributed Processing: Explorations in the Microstructure of Cognition, Volume 2: Psychological and Biological Models, J. L. McClelland, D. E. Rumelhart, PDP Research Group, Eds. (MIT Press/Bradford Books, Cambridge, MA, 1986), pp. 216-271; S. Pinker and J. Mehler, E......

2. A. Prince and P. Smolensky, Notes on Connectionism and Harmony Theory in Linguistics. ( Technical Report, Department of Computer Science, University of Colorado, Boulder, CO, 1991); Optimality Theory: Constraint Interaction in Generative Grammar ( Technical Report, Rutgers Center for Cognitive Science, Rutgers University, New Brunswick, NJ and Department of Computer Science, University of Color......

3. Selected basic sources: Formal universalism: N. Chomsky, Aspects of the Theory of Syntax (MIT Press, Cambridge, MA, 1965); and M. Halle, The Sound Pattern of English (Harper and Row, New York, 1968). Substantive process and product universalism: D. Stampe, A Dissertation on Natural Phonology (Garland, New York, 1979); D. Perlmutter, Ed., Studies in Relational Grammar 1 (Univ. of Chicago Press, ......

4. R. Jakobson, Selected Writings I (Mouton, The Hague, 1962); N. Trubetzkoy, Grundzuš ge der Phonologie (1939; translation: Principles of Phonology, Univ. of California Press, Berkeley, CA, 1969); N. Chomsky and M. Halle, The Sound Pattern of English (Harper and Row, New York, 1968), chapter 9.

5. For details, see B. Tranel, French Liaison and Elision Revisited: A Unified Account Within Optimality Theory (ROA-15, http://ruccs.rutgers.edu/roa.html, 1994).

6. For significant extensions of FAITHFULNESS within optimality theory, see J. McCarthy and A. Prince, in The Prosody-Morphology Interface, R. Kager, W. Zonneveld, H. van der Hulst, Eds. (Blackwell, Oxford, UK, in press); L. Benua, in Papers in Optimality Theory, J. Beckman, L. Walsh Dickey, S. Urbanczyk, Eds. (Linguistics Department, Univ. of Massachusetts, Amherst, MA, 1995), pp. 77-136.

7. Examples include segmental repertories, stress patterns, vowel harmony, tonology, reduplicative and templatic morphology, syntax-phonology and morphology-phonology relations, case and voice patterns, principles of question formation, interaction of syntactic movement and clause patterns, structure of verbal complexes, order and repertory of clitic elements, the interaction between focus and the......

8. P. Smolensky, Behav. Brain Sci. 11, 1 (1988); S. Pinker and A. Prince, Cognition 28, 73 (1988); M. McCloskey, Psychol. Sci. 2, 387 (1991); A. Prince, In Defense of the Number i: Anatomy of a Linear Dynamical Model of Linguistic Generalizations ( Technical Report RuCCS-TR-1, Rutgers Center for Cognitive Science, Rutgers University, New Brunswick, NJ, 1993).

9. J. J. Hopfield, Proc. Natl. Acad. Sci. U.S.A. 79, 2554 (1982); M. A Cohen and S. Grossberg, IEEE Trans. Syst. Man Cybernet. 13, 815 (1983); P. Smolensky, Proc. Natl. Conf. Artif. Intell. AAAI-83, 378 (1983); G. E. Hinton and T. J. Sejnowski, Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (1983), p. 448; J. J. Hopfield, Proc. Natl. Acad. Sci. U.S.A......

10. P. Smolensky, in Parallel Distributed Processing: Explorations in the Microstructure of Cognition, Volume 1: Foundations, D. E. Rumelhart, J. L. McClelland, PDP Research Group, Eds. (MIT Press/Bradford Books, Cambridge, MA, 1986), pp. 194-281.

11. R. Pike, Psychol. Rev. 9, 281 (1984); C. P. Dolan, thesis, University of California, Los Angeles (1989); and P. Smolensky, Connection Sci. 1, 53 (1989); P. Smolensky, Artif. Intell. 46, 159 (1990); T. Plate, thesis, University of Toronto (1994).

12. G. Legendre, Y. Miyata, P. Smolensky, Proc. Annu. Conf. Cognit. Sci. Soc. 12, 388, (1990); ibid., p. 884.

13. B. Tesar and P. Smolensky, Linguist. Inq., in press; Learnability in Optimality Theory ( Technical Report, Cognitive Science Department, Johns Hopkins University, Baltimore, MD, 1996).

14. P. Smolensky, Linguist. Inq. 27, 720 (1996).

15. L. E. Baum and T. Petrie, Ann. Math. Stat. 37, 1559 (1966); L. R. Bahl, F. Jelinek, R. L. Mercer, IEEE Trans. Pattern Anal. Mach. Intell. PAMI-5 (1983), pp. 179-190. For recent review articles, see A. NaŽ das and R. L. Mercer, in Mathematical Perspectives on Neural Networks, P. Smolensky, M. C. Mozer, D. E. Rumelhart, Eds. (LEA, Mahwah, NJ, 1996), pp. 603- 650; P. Smolensky, in ibid., pp. 453-......

16. B. Tesar, Lingua, in press.

17. References in (13) and B. Tesar and P. Smolensky, The Learnability of Optimality Theory: An Algorithm and Some Basic Complexity Results (Technical Report, Department of Computer Science, University of Colorado, Boulder, CO, 1993).

18. As indicated in the cited publications, much of the work discussed here was carried out jointly with our collaborators G. Legendre, J. McCarthy, and B. Tesar; we are grateful to them and to our colleagues L. Burzio, R. Frank, J. Grimshaw, and C. Wilson for stimulating conversations and invaluable contributions. For support of the work presented here, we acknowledge a Guggenheim Fellowship, the......