Functions Definable by Numerical Set-Expressions

Details Functions Definable by Numerical Set-Expressions Functions Definable by Numerical Set-Expressions

2009-10-31

arxiv.org/abs/0911.0105v1

Computer Science

Logic in Computer Science

Scientific paper

A "numerical set-expression" is a term specifying a cascade of arithmetic and logical operations to be performed on sets of non-negative integers. If these operations are confined to the usual Boolean operations together with the result of lifting addition to the level of sets, we speak of "additive circuits". If they are confined to the usual Boolean operations together with the result of lifting addition and multiplication to the level of sets, we speak of "arithmetic circuits". In this paper, we investigate the definability of sets and functions by means of additive and arithmetic circuits, occasionally augmented with additional operations.

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