Algebraic proof systems reduce computational problems to problems about estimating the distance of a sequence of functions $u=(u_1,\ldots, u_k)$, given as oracles, from a linear error correcting code $V$. The soundness of such systems relies on methods that act ``locally'' on $u$ and map it to a single function $u^*$ ... more >>>

Suppose Alice and Bob are communicating bits to each other in order to compute some function $f$, but instead of a classical communication channel they have a pair of walkie-talkie devices. They can use some classical communication protocol for $f$ where each round one player sends bit and the other ... more >>>

In the seminal work of \cite{Babai85}, Babai have introduced \emph{Arthur-Merlin Protocols} and in particular the complexity classes $MA$ and $AM$ as randomized extensions of the class $NP$. While it is easy to see that $NP \subseteq MA \subseteq AM$, it has been a long standing open question whether these classes ... more >>>