Complex Algebras of Arithmetic

被引：0

作者：

Duentsch, Ivo ^{[1
]}

Pratt-Hartmann, Ian ^{[2
]}

机构：

[1] Brock Univ, Dept Comp Sci, St Catharines, ON LS2 3A1, Canada

[2] Univ Manchester, Dept Comp Sci, Manchester M13 9PL, Lancs, England

来源：

FUNDAMENTA INFORMATICAE | 2009年 / 97卷 / 04期

基金：

英国工程与自然科学研究理事会; 加拿大自然科学与工程研究理事会;

关键词：

MEMBERSHIP PROBLEMS; SETS; CIRCUITS; EQUATIONS;

D O I：

10.3233/FI-2009-206

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

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.

引用

页码：347 / 367

页数：21

共 17 条

[1]

BAKER KA, 1977, ADV MATH, V24, P207, DOI 10.1016/0001-8708(77)90056-1

[2]

BAYASGALAN B, 1988, ALGEBRAIC SYSTEMS TH, P4

[3] On the structure of abstract algebras [J].

Birkhoff, G .

PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1935, 31 :433-454

[4]

Burris S., 1981, A Course in Universal Algebra, Graduate Texts in Mathematics, 78

[5]

Glasser C, 2007, LECT NOTES COMPUT SC, V4855, P253

[6] VARIETIES OF COMPLEX ALGEBRAS [J].

GOLDBLATT, R .

ANNALS OF PURE AND APPLIED LOGIC, 1989, 44 (03) :173-242

[7]

Jez A, 2008, LECT NOTES COMPUT SC, V5126, P63

[8]

JIPSEN P, 1992, THESIS VANDERBILT U

[9]

Jnsson Bjarni., 1951, American Journal of Mathematics, V73, P891, DOI DOI 10.2307/2372123

[10]

Koppelberg S., 1989, HDB BOOLEAN ALGEBRAS, V1

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