The strongest known lower bound for circuits over the basis U2 is 5n − o(n). This bound is proved by Iwama and Morizumi53 for (n − o(n))-mixed 9 Page 24 functions. Amano and Tarui6 construct an (n − o(n))-mixed function whose circuit complexity over U2 is 5n + o(n).
where U 2 = B 2 ∖ { ⊕ , ≡ }. This implies a 7n lower bound on the circuit complexity over U 2 of f 1, …, f n if f has circuit complexity at least 5n.
The main purpose of this paper is to give a better lower bound for the following case. Let f:{0,1} n →{0,1} and f i =f⊕x i for 1≤i≤n. Assume that f ...
A circuit of the smallest size in U2 contains only binary functions and variables so every binary function f of two variables g1,g2 in U2 can be presented as f ...
If g(x, y) U2, then there exists a constant c {0, 1} such that g(c, y) is a constant. We say that the constant c blocks the function g. Note that this property ...
bounds on circuit size for functions in ”P. • Best we ve been able to show is exponential lower bounds on constant depth circuits. • References: J urst,Saxe ...
Lower bounds to formula size also produce lower bounds to circuit depth, a measure of the parallel time needed for a function. Research on these restricted ...
In this paper we consider Boolean circuits over the full binary basis. A simple counting argument [1] shows that most Boolean functions require circuits of ...
Mar 6, 2014 · Blum's 3n−o(n) lower bound is the best known circuit lower bound over the complete basis for an explicit function f:{0,1}n→{0,1}, cf. Jukna's ...
Shannon's lower bound: Almost every n-ary boolean function has circuit size > 2n/n. A corollary of the Lupanov and Shannon bounds is the ...