Size of OBDD representation of 2-level redundancies functions

Abstract

We consider an explicit boolean function depending on $\text{n}\text{=}\text{(i+1)j}$ variables encoding 2-level cascade redundancies in critical systems. We establish lower and upper bounds on the size of its OBDD representation. The exact lower bound of this function is comprised between $\text{Ω(2}{}^{\mathrm{<mtext>min</mtext><mtext>(i/2,1ptj/2)</mtext>}}\text{)}$ and $\text{O}\text{(2}{}^{\mathrm{<mtext>min</mtext><mtext>(i,1ptj)</mtext>}}\text{)}$. The upper bound is . We further show that, when one of the parameters $\text{i}$ or $\text{j}$ is constant, this function admits OBDDs whose size is polynomial in other parameter. The latter result is constructive, and we show variable orderings that witness this polynomial size.