In their paper on the "chasm at depth four", Agrawal and Vinay have shown that polynomials in m variables of degree O(m) which admit arithmetic circuits of size 2o(m) al...
In this paper we give the first deterministic polynomial time algorithm for testing whether a diagonal depth-3 circuit C(x1, . . . , xn) (i.e. C is a sum of powers of linear funct...
In this note, we use lower bounds on Boolean multiplicative complexity to prove lower bounds on Boolean circuit complexity. We give a very simple proof of a 7n/3 − c lower bound ...
An exponential lower bound on the circuit complexity of deciding the weak monadic second-order theory of one successor (WS1S) is proved. Circuits are built from binary operations, ...