On an interesting hypothesis of the theory of formal languages

Document Type : Original Article

Author

Shenzhen MSU-BIT University

10.22061/jdma.2024.10789.1069

Abstract

The formulation of a hypothesis for any pair of nonempty finite languages is considered. The hypothesis consists in the formulation of the necessary conditions for the equality of infinite iterations of these languages, the paper provides some equivalent versions of this hypothesis. When fulfilling this hypothesis, we show the possibility of verifying the equality of infinite iterations of these languages in polynomial time. On the other hand, we present a plan for reducing the verification of the same equality to checking the completeness of the language of a specially constructed nondeterministic finite automaton, and such a check cannot be carried out in polynomial time. In this regard, the possibility of reducing the equality P=NP to the special hypothesis of the theory of formal languages is formulated.

Keywords

Main Subjects