I am generating random DFAs to test a DFA reduction algorithm on them. The algorithm that I'm using right now is as follows: for each state $q$, for each symbol in the alphabet $c$, add $\delta (q, ...
For a random undirected graph with $n$ nodes, where each node has $k$ incident edges ($nk/2$ edges in total), the vertex set is partitioned into two sets each having $n/2$ nodes. What is the ...
Let Alice and Bob be two users chosen uniformly at random from a social network (e.g. Facebook). What is the probability that they are friends assuming that they share $k$ mutual friends? I am ...
There is a family of random graphs $G(n, p)$ with $n$ nodes (due to Gilbert). Each possible edge is independently inserted into $G(n, p)$ with probability $p$. Let $X_k$ be the number of cliques of ...