Complex Algebras of Arithmetic

Article type: Research Article

Authors: Düntsch, Ivo | Pratt-Hartmann, Ian

Affiliations: Department of Computer Science, Brock University St. Catharines, ON, L2S 3A1, Canada. E-mail: [email protected] | Department of Computer Science, University of Manchester, Oxford Road, Manchester, United Kingdom. E-mail: [email protected]

Abstract: An arithmetic circuit is a labeled, acyclic directed graph specifying a sequence of arithmetic and logical operations to be performed on sets of natural numbers. Arithmetic circuits can also be viewed as the elements of the smallest subalgebra of the complex algebra of the semiring of natural numbers. In the present paper we investigate the algebraic structure of complex algebras of natural numbers and make some observations regarding the complexity of various theories of such algebras.

DOI: 10.3233/FI-2009-206

Journal: Fundamenta Informaticae, vol. 97, no. 4, pp. 347-367, 2009