In the first part of the talk, state-of-the-art time-space tradeoff lower bounds for unrestricted branching programs (or, equivalently, RAM algorithms) have been surveyed and some remarks about proof techniques have been made. In the second part, a lower bound on the size of randomized read-$k$ BPs of order $2^{-\Omega(k^{-2}2^{-13k}n}$ for the function $\textrm{cl}_{3,n}$ testing whether a graph on $n$ nodes has a $3$-clique has been presented that works if the error probability is bounded by $O(2^{-4k})$. The best previous bound for this function (Sauerhoff, 2003) was of order $2^{-\Omega(k^{-2}2^{4k}\sqrt{n}}$ and required an upper bound on the error of $2^{-\Theta(2^{-2k})}$. The function can be trivially computed even by nondeterministic OBDDs of size $O(n^3)$ by a straightforward
guess-and-verify approach.