On equations over sets of numbers and their limitations

Tommi Lehtinen, Alexander Okhotin

Результат исследований: Научные публикации в периодических изданияхстатьярецензирование

7 Цитирования (Scopus)

Аннотация

Systems of equations of the form X = Y + Z and X = C, in which the unknowns are sets of natural numbers, "+" denotes elementwise sum of sets S + T = {m + n | m ∈ S, n ∈ T}, and C is an ultimately periodic constant, have recently been proved to be computationally universal (Jeż, Okhotin, "Equations over sets of natural numbers with addition only", STACS 2009). This paper establishes some limitations of such systems. A class of sets of numbers that cannot be represented by unique, least or greatest solutions of systems of this form is defined, and a particular set in this class is constructed. The argument is then extended to equations over sets of integers.

Язык оригиналаанглийский
Страницы (с-по)377-393
Число страниц17
ЖурналInternational Journal of Foundations of Computer Science
Том22
Номер выпуска2
DOI
СостояниеОпубликовано - фев 2011
Опубликовано для внешнего пользованияДа

Предметные области Scopus

  • Компьютерные науки (разное)

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