中英對照讀新聞》Decades-Old Computer Science Conjecture Solved in Two Pages 以兩頁證出數十年懸而未解的計算機科學猜想

證出「布林函數敏感度猜想」的數學家黃皓。（取自網路）

◎劉宜庭

A paper posted online this month has settled a nearly 30-year-old conjecture about the structure of the fundamental building blocks of computer circuits. This "sensitivity" conjecture has stumped many of the most prominent computer scientists over the years, yet the new proof is so simple that one researcher summed it up in a single tweet.

一篇本月線上公開的論文已證出近30年懸而未解、有關計算機電路組件架構的數學猜想。這項「敏感度猜想」多年來難倒許多傑出的計算機科學家，但甫出爐的證明相當簡潔，研究員甚至可以僅用一條「推特」概述。

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The conjecture concerns Boolean functions, rules for transforming a string of input bits（0s and 1s）into a single output bit. One such rule is to output a 1 provided any of the input bits is 1, and a 0 otherwise; another rule is to output a 0 if the string has an even number of 1s, and a 1 otherwise.

這項猜想關乎「布林函數」將輸入位元串（0或1）轉換成單一輸出位元的規則。其中包括，若輸出為1，則至少任一輸入位元是1，否則輸出為0；若輸出為0，則輸入位元串有偶數個位元1，否則輸出為1。

Hao Huang, a mathematician at Emory University, has proved the sensitivity conjecture with an ingenious but elementary two-page argument about the combinatorics of points on cubes.

美國艾莫瑞大學的數學家黃皓，透過兩頁巧妙但基本的論證式，解答出有關立方體頂點的組合數學問題，進而證出「敏感度猜想」。

In 2018, Huang used a 200-year-old piece of mathematics called the Cauchy interlace theorem, which relates a matrix’s eigenvalues to those of a submatrix, making it potentially the perfect tool to study the relationship between a cube and a subset of its corners.

黃皓在2018年使用已有200年歷史的「柯西交錯定理」，勾串矩陣的特徵值及其子矩陣，讓該定理成為研究立方體及其頂點子集合的絕佳工具。

新聞辭典

Boolean function：名詞，布林函數。例句：Every computer circuit is some combination of Boolean functions.（每個計算機電路都是某種布林函數的組合。）

conjecture：名詞，臆測、猜想、推測。例句：There’s been a lot of conjecture in the media recently about the marriage.（媒體近期對這樁婚姻大加臆測。）

sensitivity：名詞，靈敏度、敏感度。例句：The sensitivity of the machine provides us with extremely accurate data.（這台機器的高靈敏度可為我們提供極精確的數據。）

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