On the number of nonterminal symbols in unambiguous conjunctive grammars

Результат исследований: Научные публикации в периодических изданияхстатья

Аннотация

Unambiguous conjunctive grammars with 1 nonterminal symbol are shown to be strictly weaker than the grammars with 2 nonterminal symbols, which are in turn strictly weaker that the grammars with 3 or more nonterminal symbols. This hierarchy is established by considering grammars over a one-symbol alphabet, for which it is shown that 1-nonterminal grammars describe only regular languages, 2-nonterminal grammars describe some non-regular languages, but all of them are in a certain sense sparse, whereas 3-nonterminal grammars may describe some non-regular languages of non-zero density. It is also proved that one can test a 2-nonterminal grammar for equivalence with a regular language, whereas the equivalence between a pair of 2-nonterminal grammars is undecidable.

Язык оригиналаанглийский
Страницы (с-по)43-72
Число страниц30
ЖурналFundamenta Informaticae
Том162
Номер выпуска1
DOI
СостояниеОпубликовано - 1 янв 2018

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  • Теоретические компьютерные науки
  • Алгебра и теория чисел
  • Информационные системы
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