The states of "M" (described by the position of its head on the input tape and the configuration of the log-space working memory) can be thought of as the vertices of a directed graph, and the transitions of "M" can be thought of as edges in this graph. "M" accepts an input string whenever there exists a path in this graph from the vertex that represents the starting state to a special vertex that represents any accepting state. In this way, the existence of an accepting nondeterministic computation for "M" can be seen as a version of the -connectivity problem, for implicit graphs rather than graphs given explicitly as an explicitly-represented input graph. In this graphical view, the goal of the proof is to find a nondeterministic logspace algorithm that accepts only when there does "not" exist a path from to in the same implicit graph.