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

2026/02/20 by Krasimir Yordzhev · 1 voice
Computer Science · Mathematics · #cs.FL #math.CO

paper · pdf · doi:10.2298/fil2412157y

Abstract

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 semiring S_U whose elements are the set 2^U of all subsets of U and with operations - product and union of the elements of 2^U. The described algorithm executes no more than O(n³) operations in S_U.

Citations

• Inclusion of regular and linear languages in group languages
• A representation of context-free grammars with the help of finite digraphs
• Introduction to automata theory, languages, and computation, 2nd edition

Discussions

• Krasimir Yordzhev: On A. V. Anisimov's problem for finding a polynomial algorithm checking inclusion of context-free languages in group languages https://arxiv.org/abs/2602.18305 https://arxiv.org/pdf [bsky, 0 points, 0 comments]

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