Path Dialect

shows a traversal across Fences rather than through Doors.

This dialect represents potential parellelism as diverging paths, however the Traversal Metaphor suggests that we must choose one path and backtrack to explore the other path.

Uninformed choice of one path over another is the hallmark of a complex algorithmic process. Polynomial processes (P) do not require Backtracking, while exponential processes (NP) do.

Paths end at units along the round border and at constants along the square border. Labeled variables lying on the round or square border identify subpaths with their own internal structure. Paths provide a unique parity count of crossings. They structurally distinguish odd and even depths of nestings.

When a path terminates at a variable or constant on both sides of a border, the form is *Binate*, another inherent marker of computational complexity.