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- W1590187530 abstract "A finite recurrent system over the power set of the natural numbers of dimension n is a pair composed of nn-ary functions over the power set of the natural numbers and an n-tuple of singleton sets of naturals. Every function is applied to the components of the tuple and computes a set of natural numbers, that might also be empty. The results are composed into another tuple, and the process is restarted. Thus, a finite recurrent system generates an infinite sequence of n-tuples of sets of natural numbers. The last component of a generated n-tuple is the output of one step, and the union of all outputs is the set defined by the system. We will consider only special finite recurrent systems: functions are built from the set operations union (∪), intersection (∩) and complementation (–) and the arithmetic operations addition (⊕) and multiplication (⊗). Sum and product of two sets of natural numbers are defined elementwise. We will study two types of membership problems: given a finite recurrent system and a natural number, does the set defined by the system contain the queried number, and does the output of a specified step contain the queried number? We will determine upper and lower bounds for such problems where we restrict the allowed operations to subsets of {∩,∪,−−,⊕,⊗}. We will show completeness results for the complexity classes NL, NP and PSPACE." @default.
- W1590187530 created "2016-06-24" @default.
- W1590187530 creator A5018511843 @default.
- W1590187530 date "2005-01-01" @default.
- W1590187530 modified "2023-09-23" @default.
- W1590187530 title "Decidable Membership Problems for Finite Recurrent Systems over Sets of Naturals" @default.
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- W1590187530 doi "https://doi.org/10.1007/11537311_8" @default.
- W1590187530 hasPublicationYear "2005" @default.
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