A light transport simulator and a method of constructing and classifying light transport paths. One embodiment of the light transport simulator includes a light transport simulator operable to construct and classify a light transport path between two points in a scene, including: (1) a memory configured to store dual deterministic finite automata (DFA) based on an LPE that defines criteria for accepting the light transport path, and (2) a processor configured to employ the dual DFA to construct opposing light subpaths originating from the two points, and employ a correspondence among states of the dual DFA to unite the opposing light subpaths to form the light transport path.