Example: PATH decision problem language

PATH = {$\langle$G, u, v, k$\rangle$$\mid$ G = (V, E) is a directed graph, u, v $\in$ V, k $\geq$ 0 is an integer, and there exists a path from u to v in G whose length is at most k}

Note that the problem $\langle$G, u, v, k$\rangle$ is encoded as a binary string.