Suppose I want to have an integer program for handling the cases

  1. $x_1>1\wedge x_2>1\wedge x_3>1\wedge\dots\wedge x_n>1\iff\delta=1$

  2. $x_1>1\vee x_2>1\vee x_3>1\vee\dots\vee x_n>1\iff\delta=1$

how many number of integer variables are needed to handle case?

Is it possible at least one of them needs at most a constant number of binary variables?

  • $\begingroup$ What encoding have you tried? How many binary variables do you get? Why is it hard to construct one with less variables? $\endgroup$ – Discrete lizard Apr 3 at 6:04

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