See Loop analysis
Derived using Topological trace formula
gives topological polynomial, which is just the characteristic polynomial of the transition matrix
https://qchu.wordpress.com/2009/11/17/the-lindstrom-gessel-viennot-lemma/
https://math.stackexchange.com/questions/13754/graph-theoretic-interpretation-of-determinant
https://mathoverflow.net/questions/134956/determinants-in-graph-theory
Examples from fsts. See notebook and here
FST 10
http://www.wolframalpha.com/input/?i=1-3z%5E2%3D0
Can analyze forward or backward
FST 21