We outline an implementation of Viterbi beam search that incorporates layered bigrams. Layered bigrams are class bigrams in which some nodes are themselves bigrams, resulting in a recursive structure. The implementation is in C++ and involves a hierarchy of classes. The paper outlines the main concepts and the corresponding C++ classes.

We develop a description of spin waves in $3D$ quantum $XY$ antiferromagnet (AFM) terms macroscopic variables, magnetization and N\'eel vector densities. consider layered AFM with spins located on the honeycomb lattice. In discussed system, spectrum consists four modes, all well captured by our description. The gapless mode waves, i.e., magnons, is described system equations, which has structur...