The bounded degree problem for NLC grammars is decidable

摘要

The degree of a graph H is the maximum among the degrees of its nodes. A set of graphs L is of bounded degree if there exists a positive integer n such that the degree of each graph in L does not exceed n. We demonstrate that it is decidable whether or not the (graph) language of an arbitrary node label controlled (NLC) grammar is of bounded degree. Moreover, it is shown that, given an arbitrary NLC grammar G generating the language L(G) of bounded degree, one can effectively compute the maximum integer which appears as the degree of a graph in L(G).