http:^^www.das.harvard.edu^users^faculty^leslie_valiant^leslie_valiant.html

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Date: Wed, 20 Nov 1996 22:57:17 GMTServer: NCSA/1.5Content-type: text/htmlLast-modified: Thu, 10 Nov 1994 20:37:22 GMTContent-length: 2856<HTML><HEAD><title>Leslie G. Valiant</title></HEAD><BODY><h1>Leslie Valiant</h1><!WA0><img align=top src=http://www.das.harvard.edu/users/faculty/Leslie_Valiant/Leslie_Valiant.gif><h3>Gordon McKay Professor of Computer Science and Applied Mathematics</h3><h3>THEORY OF COMPUTATION AND MACHINE LEARNING</h3><p>Complexity theory, the study of the fundamental laws and limitationsthat govern computations, is not only an inherently rich mathematicalsubject but one whose conclusions and methodology are increasinglyrelevant to practical computational problems.  Professor Valiant'sresearch is focused on two application areas, machine learning andparallel computation, as well as the core area.<p>A machine that has a learning capability can augment its knowledge byinteracting with its environment; no programmer need understand themachine's present, possibly unmanageably complicated state ofknowledge.  The goals of Professor Valiant's current research are toderive models that capture the phenomenon of learning, particularly thelearning of concepts from examples, and to use these models to identifyefficient learning algorithms, as well as the ultimate limits tocomputational learning.  For example, in the area of parallelcomputation, how efficient and easy to program can general purposemachines be made?  In this connection, Professor Valiant and hiscolleagues have obtained some encouraging results concerning thepossibility of constructing general-purpose, multiprocessor computerscapable of executing parallel algorithms in close to logically optimaltime.  They are also searching for efficient or optimal parallelalgorithms for important computational problems.<p>In the core area of complexity theory, relationships of surprisinggenerality can sometimes be obtained.  For example, relationshipshave been found between the difficulty of finding solutions tocombinatorial problems in the case when a unique solution isguaranteed to the more general case when it is not; other work relatesthe problem of randomly generating one solution, from possiblyexponentially many, to the problem of counting these solutions.<hr><ul><li><i>A theory of the learnable,</i> Commun. Assoc. Comp. Mach. 27, 1136 (1984).<li>M. R. Jerrum, L. G. Valiant, and V. V. Vazirani, <i>Random generation of combinatorial structures from a uniform distribution,</i>Theor. Comp. Sci. 43, 169-188 (1986).<li><i>Functionality in neural networks,</i> in Proc. 7th Natl. AAAIConf. on Artificial Intelligence, (Morgan Kaufmann, San Mateo,Calif., 1988), p. 629-634.<li>M. Kearns and L. G. Valiant, <i>Cryptographic limitations on learning Boolean formulae andfinite automata,</i> Proc. 21st ACM Symp. on Theory of Computing,(ACM Press, New York, 1989), p. 433-444. <li><i>A bridging model for parallel computation,</i>Commun. Assoc. Comp. Mach. 33, 103-111 (1990).</ul></BODY></HTML>

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