The paper is devoted to the development of an algorithm for constructing a context-free grammar for multigraph pushdown automaton (PDA).

Development of an algorithm is based on the idea of representation the PDA as a directed multigraph. This approach optimizes context -free grammar (CFG), which can be obtained by the known algorithm using the program of PDA.

The algorithm for constructing optimized CFG is based on the enumeration of certain paths in the multigraph. A method is similar to the standard depth-first search in a directed graph. Proposed method lists so-called balanced ways, the passage of which corresponds to reading the input word by PDA until it passes a sequence of states from the initial state to the final state with the devastation store, thus allowing the input word. This frees CFG equivalent to this PDA from useless nonterminals and ensure causing all strings allowed PDA. Thus, a CFG being constructed by the algorithm will generate exactly the language that allowed by the PDA. In addition, the algorithm presented in the article can be considered as the generative model of the language permitted by PDA.

The main result of this paper is design of the algorithm for constructing optimized CFG starting with the PDA multigraph. A description of the algorithm is given using the pseudocode. It is shown that calculated upper bound for the algorithm complexity is of the cubic order of the number of the multigraph edges.

PDA multigraphs are discussed in several papers. But mostly, multigraphs are used solely as an illustration. In this paper a multigraph is used not only as a visual representation of PDA, but as a working model, which is defined in terms of the language of PDA. The equivalence of such a model to the known models is proved too.

Thus, the paper proposes an efficient algorithm for enumerating paths in a directed multigraph, on the basis of which it is possible to build an optimized CFG equivalent to the original PDA.

Among the tasks which will continue the started study there is a more accurate upper bound finding on the algorithm complexity.