On A. V. Anisimov's problem for finding a polynomial algorithm checking inclusion of context-free languages in group languages

The work investigates the problem of whether a context-free language is a subset of a group language. A. V. Anisimov has shown that the problem of determining the unambiguity of finite automata is a special case of this problem. Then the question of finding polynomial algorithm verifying the inclusion of context-free languages in group languages naturally arises. The article focuses on this open problem. For the purpose, the paper describes an unconventional method of description of context-free languages, namely a representation with the help of a finite digraph whose arcs are labelled with a specially defined monoid U. Also, we define a semiUring SU whose elements are the set 2U of all subsets of U and with operations-product and union of the elements of 2U. The described algorithm executes no more th3an O(n3) operations in SU.