Communication complexity is the mathematical study of scenarios where several parties
need to communicate to achieve a common goal, a situation that naturally appears during …

From the winner of the Turing Award and the Abel Prize, an introduction to computational
complexity theory, its connections and interactions with mathematics, and its central role in …

We give a new and improved proof that the shrinkage exponent of De Morgan formulae is 2.
Namely, we show that for any Boolean function f:{0, 1} n→{0, 1}, setting each variable out of …

One of the major challenges of the research in circuit complexity is proving super-polynomial
lower bounds for de Morgan formulas. Karchmer et al.(Comput Complex 5 (3/4): 191–204 …

One of the major open problems in complexity theory is proving super-logarithmic lower
bounds on the depth of circuits (ie, P\nsubseteqNC^1). Karchmer, Raz, and Wigderson …

In the communication problem UR (universal relation)[25], Alice and Bob respectively
receive x, y∈{0, 1} n with the promise that x≠ y. The last player to receive a message must …

A de Morgan formula over Boolean variables x 1,…, xn is a binary tree whose internal nodes
are marked with AND or OR gates and whose leaves are marked with variables or their …

One of the major open problems in complexity theory is proving superlogarithmic lower
bounds on the depth of circuits (ie, P\not⊆NC^1). This problem is interesting for two …

We show a deterministic simulation (or lifting) theorem for composed problems f◦ Eqn where
the inner function (the gadget) is Equality on n bits. When f is a total function on p bits, it is …

The best known size lower bounds against unrestricted circuits have remained around $3 n
$ for several decades. Moreover, the only known technique for proving lower bounds in this …