Michael Levin

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Michael Levin, an American computer scientist, in the 60s affiliated with Massachusetts Institute of Technology, and involved in the initial development of Lisp within the group of John McCarthy. The 1961 memo on Alpha-Beta by Daniel Edwards and Timothy Hart, contains a Theorem by Michael Levin, the well known formula of the number of leaf nodes that need to be examined in Alpha-Beta.

=Theorem= Theorem (Levin): Let n be the number of plies in a tree, and let b be the number of branches a every branch point. Then the number of terminal points on the tree is T = b n However, if the best possible advantage is take of the alpha-beta heuristic then the number of terminal points that need to be examined is for odd n, T = b (n+1)/2 + b (n-1)/2 - 1 and for even n, T = 2b n/2 - 1 which can be reformulated for both cases using ceil and floor functions: T = b &#8968;n/2&#8969; + b &#8970;n/2&#8971; - 1

=Quotes=

LISP
=See also=
 * History of Alpha-Beta
 * Leaves from Node Types
 * LISP
 * Odd-Even Effect

=Selected Publications=
 * John McCarthy, Paul W. Abrahams, Daniel J. Edwards, Timothy P. Hart, Michael I. Levin (1962). LISP 1.5 Programmer's Manual. The M.I.T. Press, second edition (1985) available as pdf reprint
 * Michael Levin (1963). Primitive Recursion, AIM-055, reprint available from DSpace at MIT
 * Timothy Hart, Michael Levin (1964). LISP Exercises, AIM-064, reprint available from DSpace at MIT
 * Michael Levin (1964). Syntax of the New Language, AIM-068, reprint available from DSpace at MIT
 * Michael Levin (1964). New Language Storage Conventions, AIM-069, reprint available from DSpace at MIT

=References=

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