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Article information
2013 , Volume 18, ¹ 4, p.48-63
Smetanin Y.G., Ulyanov M.V.
Algebraic structure with partial operations and computational model for the arithmetic of bounded nonnegative numbers
A mathematical framework for computer integer arithmetic is proposed. The framework is based on the original algebraic structure with partial operations (that is, operations with bounded set of feasible operands). For the constructive implementation of the proposed algebraic structure, a model of computation with preconditions of the execution of the instructions is proposed. The proposed model is a formal model of a computer with bounded integer arithmetic. Algorithms that implement the operations of the algebraic structure are presented using elementary operations of the proposed computation model. The model is shown to be applicable for the problems of testing the feasibility and eliminating singularities of input arithmetic clauses using equivalent transformations of their representing polynomials.
[full text]
Keywords: model of computation, preconditions of instructions, partial algebras, bounded arithmetic, equivalent transformations of polynomials
Author(s):
Smetanin Yury Gennadievich
Dr.
Position: General Scientist
Office: Dorodnicyn Computing Center of the Russian Academy of Science
Address: Russia, Moscow
E-mail: smetanin.iury2011@yandex.ru
Ulyanov Mikhail Vasilievich
Dr. , Professor
Position: Professor
Office: V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Lomonosov Moscow State University
Address: 117997, Russia, Moscow, 65 Profsoyuznaya street
Phone Office: (495) 334-89-10
E-mail: muljanov@mail.ru
Bibliography link:
Smetanin Y.G., Ulyanov M.V. Algebraic structure with partial operations and computational model for the arithmetic of bounded nonnegative numbers // Computational technologies. 2013. V. 18. ¹ 4. P. 48-63
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