Alpha-Beta pruning

Abstract

One of the most apparently subtle techniques taught in a typical Al survey course is minimaxing with alpha-beta pruning. As Winston writes in his text: "It is not unusual to get lost in this.... Even seasoned game specialists still feel magic in the alpha-beta procedure. Each individual conclusion seems right, but somehow the global result is strange." One way of lessening the apparent mystery of the technique is to ground it in something virtually every computer science student has seen and mastered earlier: cutoff of evaluation in conditionals. After encountering a true disjunct or a false conjunct in thre protasis of an IF statement a reasonable compiler will cease evaluation and return true and false respectively. It is easy to see by constructing some quick truth tables that the MAX function and disjunction are the same. Likewise, the MIN function and conjunction are equivalent. To stop evaluation of a MAX function, what occurs in alpha-beta pruning, is thus no different from what happens to everyday compound conditions with a disjunction. <u>Mutatis mutandis</u>, the same thing can be said of the MIN function and conjunction. There is one slight difference, however. Ordinary conditionals are based on standard, two-state logic, while the MAX and MIN functions in minimaxing can take on many values. We thus have to complete our comparison by noting that for multi-valued logics a true statement is as true as its truest disjunct, while a false statement is as false as its falsest conjunct.