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Further Remarks on the Operational Nonterminal Complexity
International Journal of Foundations of Computer Science ( IF 0.6 ) Pub Date : 2021-01-30 , DOI: 10.1142/s0129054121410021
Jürgen Dassow 1
Affiliation  

For a regular language L, let Var(L) be the minimal number of nonterminals necessary to generate L by right linear grammars. Moreover, for natural numbers k1,k2,,kn and an n-ary regularity preserving operation f, let the range gfVar(k 1,k2,,kn) be the set of all numbers k such that there are regular languages L1,L2,,Ln with Var(Li) = ki for 1 i n and Var(f(L1,L2,,Ln)) = k. We show that, for the circular shift operation Circ, gCircVar(n) is infinite for all n, and we completely determine the set gCircVar(2). Moreover, we give a precise range for the left right quotient and a partial result for the left quotient. Furthermore, we add some values to the range for the operation intersection which improves the result of [2].

中文翻译:

关于操作非终端复杂性的进一步评论

对于常规语言大号, 让变量(大号)是生成所需的最小非终结符数大号通过正确的线性语法。此外,对于自然数ķ1,ķ2,,ķnn-ary正则保持操作F, 让范围GF变量(ķ 1,ķ2,,ķn)是所有数字的集合ķ使得有常规语言大号1,大号2,,大号n变量(大号一世) = ķ一世为了1 一世 n变量(F(大号1,大号2,,大号n)) = ķ. 我们证明,对于循环移位操作,G变量(n)对所有人来说都是无限的n,我们完全确定了集合G变量(2). 此外,我们给出了左商的精确范围和左商的部分结果。此外,我们在运算交集的范围内添加了一些值,从而改进了 [2]。
更新日期:2021-01-30
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