On Some Problems of Extracting the Root from a Given Finite Language

Based on the standard definition of product (concatenation), natural non-negative degree language is introduced. Root extraction reverse operation to it, and it can be defined in several different ways. Despite simplicity formulation problem extracting root, authors could not find any description literature (as well as Internet), including even its formulation. Most material this article devoted simplest version formulation: root 2nd for 1-letter alphabet, but many provisions are generalized more complex cases. Apparently, a possible future polynomial algorithm solving at least one described statements problems, first necessary really analyze detail such special case, that is: either describe algorithm, or, conversely, show belongs class NP-complete problems. Thus, article, we do propose problems under consideration; however, models here should help constructing appropriate heuristic algorithms their solution. A detailed further application beyond scope article.