On the number of nonterminals in linear conjunctive grammars

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• 作者：Okhotin ; Alexander
• 关键词：Formal languages ; Conjunctive grammar ; Trellis automaton ; Cellular automaton ; Language equation ; Descriptional complexity ; Minimal linear grammar
• 刊名：Theoretical Computer Science
• 出版年：2004
• 出版时间：June 14, 2004
• 年：2004
• 卷：320
• 期：2-3
• 页码：419-448
• 全文大小：399 K

文摘

The number of nonterminals in a linear conjunctive grammar is considered as a descriptional complexity measure of this family of languages. It is proved that a hierarchy collapses, and for every linear conjunctive grammar there exists and can be effectively constructed a linear conjunctive grammar that accepts the same language and contains exactly two nonterminals. This yields a partition of linear conjunctive languages into two nonempty disjoint classes of those with nonterminal complexity 1 and 2. The basic properties of the family of languages for which one nonterminal suffices are established. Nonterminal complexity of grammars in the linear normal form is also investigated.