We prove that the reliable computation of any Boolean function with sensitivity s requires Ω(s log s) gates if the gates of the circuit fail independently with a fixed positive...
Consider the following two-player communication process to decide a language L: The first player holds the entire input x but is polynomially bounded; the second player is computa...
This paper continues the investigation of the connection between probabilistically checkable proofs PCPs the approximability of NP-optimization problems. The emphasis is on prov...
Probabilistic (or randomized) decision trees can be used to compute Boolean functions. We consider two types of probabilistic decision trees - one has a certain probability to give...
Laura Mancinska, Maris Ozols, Ilze Dzelme-Berzina,...
While it is exponentially unlikely that a sparse random graph or hypergraph is connected, with probability 1 − o(1) such a graph has a “giant component” that, given its numbe...