Matching algorithms between a phonetic lattice and two types of templates -- Lattice and graph

We have developed two matching algorithms used in the speech recognition: (1) matching between two phonemic lattices, one for the input speech and the other for the template, and (2) matching between a phonemic lattice and a graph template. The algorithms are based on the dynamic programming. We introduced path weights proportional to the duration of lattice elements in both algorithms and loose constraints on accumulated durations in the graph-to-lattice matching. The algorithms works efficiently when the lattice elements are sorted with respect to the end times.