On language equations with concatenation and various sets of boolean operations

Результат исследований: Научные публикации в периодических изданияхстатья

Аннотация

Systems of equations of the form Xi = ℓi(X1, . . .,Xn), for 1 ≤i ≤ n, in which the unknowns Xi are formal languages, and the right-hand sides ≤i may contain concatenation and union, are known for representing context-free grammars. If, instead of union only, another set of Boolean operations is used, the expressive power of such equations may change: for example, using both union and intersection leads to conjunctive grammars [A. Okhotin, J. Automata, Languages and Combinatorics 6 (2001) 519-535], whereas using all Boolean operations allows all recursive sets to be expressed by unique solutions [A. Okhotin, Decision problems for language equations with Boolean operations, Automata, Languages and Programming, ICALP 2003, Eindhoven, The Netherlands, 239-251]. This paper investigates the expressive power of such equations with any possible set of Boolean operations. It is determined that different sets of Boolean operations give rise to exactly seven families of formal languages: the recursive languages, the conjunctive languages, the context-free languages, a certain family incomparable with the context-free languages, as well as three subregular families.

Язык оригиналаанглийский
Страницы (с-по)205-232
Число страниц28
ЖурналRAIRO - Theoretical Informatics and Applications
Том49
Номер выпуска3
DOI
СостояниеОпубликовано - 1 июл 2015

Предметные области Scopus

  • Программный продукт
  • Математика (все)
  • Прикладные компьютерные науки

Fingerprint Подробные сведения о темах исследования «On language equations with concatenation and various sets of boolean operations». Вместе они формируют уникальный семантический отпечаток (fingerprint).

Цитировать