Michael+Levin

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 * Home * People * 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.
 * Michael Levin**,

 =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

> math T = b^n math

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//,

> math T = b ^ { \frac {n+1} 2 } + b ^ { \frac {n-1} 2 } - 1 math

and for even //n//,

> math T = 2b ^{ n / 2 } - 1 math

which can be reformulated for both cases using [|ceil and floor] functions:

> math T = b^{\lceil { n / 2 } \rceil} + b^{\lfloor { n / 2 } \rfloor} - 1 math

=Quotes=

Alpha-Beta
Quote by John McCarthy from //Human-Level AI is harder than it seemed in 1955// : include page="Quote McCarthy"

LISP
Quote by John McCarthy in //From LISP 1 to LISP 1.5// : include page="Quote McCarthy on LISP" =See also=
 * History of Alpha-Beta
 * Leaves of Node Types
 * Lisp
 * Odd-Even Effect

=Selected Publications=
 * John McCarthy, Paul W. Abrahams, Daniel J. Edwards, Timothy P. Hart and 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= =What links here?= include page="Michael Levin" component="backlinks" limit="20"
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