Belousov

pp. 128-142

 The authors consider a generalization of the well-known combinatorial structure of rook polynomials for boards of arbitrary dimension. The authors obtained basic formulas and examples of their application in practice. An algorithm of computing rook polynomials was developed.

In the paper the presentation of push-down automation as oriented multigraphs is described. The language of  push-down automata, which is represented by its multigraph, is defined and equivalence of this definition with standard one is proved. In terms of this representation some properties of push-down automata (such as regularity  of  push-down stack strings set) are considered.