For a regular language L, let \({{\,\mathrm{Var}\,}}(L)\) be the minimal number of nonterminals necessary to generate L by right linear grammars. Moreover, for natural numbers \(k_1,k_2,\ldots ,k_n\) and an n-ary regularity preserving operation f, let \(g_f^{{{\,\mathrm{Var}\,}}}(k_1,k_2,\ldots ,k_n)\) be the set of all numbers k such that there are regular languages \(L_1,L_2,\ldots , L_n\) such that \({{\,\mathrm{Var}\,}}(L_i)=k_i\) for \(1\le i\le n\) and \({{\,\mathrm{Var}\,}}(f(L_1,L_2,\ldots , L_n))=k\). We completely determine the sets \(g_f^{{{\,\mathrm{Var}\,}}}\) for the operations reversal, Kleene-closures \(+\) and \(*\), and union; and we give partial results for product and intersection.

对于常规语言L，令\({{\,\mathrm{Var}\,}}(L)\)是通过右线性文法生成L所需的最小非终结符数。此外，对于自然数\(k_1,k_2,\ldots ,k_n\)和n 元正则保持运算f，让\(g_f^{{{\,\mathrm{Var}\,}}}(k_1, k_2,\ldots ,k_n)\)是所有数字k的集合，使得存在正则语言\(L_1,L_2,\ldots , L_n\)使得\({{\,\mathrm{Var}\,} }(L_i)=k_i\)对于\(1\le i\le n\)和\({{\,\mathrm{Var}\,}}(f(L_1,L_2,\ldots, L_n))= k\). 我们完全确定了集合\(g_f^{{{\,\mathrm{Var}\,}}}\)用于操作反转、Kleene-closures \(+\)和\(*\)以及联合；我们给出了乘积和交集的部分结果。