Short Tests of Closures for Contact Circuits

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 $2k+2$, respectively).