| Description |
A unate gate is a logical gate computing a unate Boolean function, which is monotone in each variable. Examples of unate gates are AND gates, OR gates, NOT gates, threshold gates etc. A unate circuit C is a combinatorial logic circuit consisting of unate gates. Let f be a symmetric Boolean function of n variables. Let m0 and m1 be the maximum number of consecutive 0s and consecutive 1s in the value vector v(f) of f, respectively. Also, let l=minm0,m1 and m=maxm0,m1. Now, let C be a unate circuit computing f. Let s be the size of the circuit C, that is, C consists of s unate gates. If we define the maximum number of gates outputting '1' over all inputs to C to be the energy e of the circuit C, then we can show that there exists a tradeoff between the size s and the energy e of C. More precisely, we will show the following - (n+1−l)/m<=se. We will also present lower bounds on the size s of a unate circuit C represented in terms of n, l and m.
|