The problem of representing Boolean functions by two-pole contact circuits that are irredundant and admit short fault detection or diagnostic tests of closures of at most k contacts for a given positive integer k is considered. The following assertions are proved: for almost every Boolean function of n variables, the minimal length of a fault detection (diagnostic) test is equal to 2 (does not exceed 2 k + 2, respectively).

中文翻译：

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接触电路闭合的短路测试

考虑用冗余的两极触点电路表示布尔函数的问题，该电路允许对给定正整数 k 的最多 k 个触点的闭合进行短路故障检测或诊断测试。证明了以下断言：对于几乎每个 n 变量的布尔函数，故障检测（诊断）测试的最小长度等于 2（分别不超过 2 k + 2）。