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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Volume 20, Number 2, Pages 311–323
(Mi timm1081)
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This article is cited in 3 scientific papers (total in 3 papers)
Quantifier-free descriptions for interval-quantifier linear systems
I. A. Sharaya Institute of Computing Technologies, Siberian Branch of the Russian Academy of Sciences
Abstract:
A system of relations of the form $Ax\,\sigma\,b$ is considered, where $\sigma$ is a relation vector with components $=$, $\geq$, and $\leq$ and the parameters (the elements of the matrix $A$ and of the right-hand side $b$) take values from given intervals. What is considered to be the set of solutions of this system depends on which quantifier is related to each interval-valued parameter and on the order of quantifier prefixes for individual parameters. For sets of solutions with a quantifier prefix of a rather general form, we obtain equivalent quantifier-free descriptions in the classical interval arithmetic, in the Kaucher interval arithmetic, and in the usual real arithmetic.
Keywords:
interval systems of linear equations and inequalities, elimination of quantifiers, Kaucher arithmetic.
Received: 18.02.2013
Citation:
I. A. Sharaya, “Quantifier-free descriptions for interval-quantifier linear systems”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 2, 2014, 311–323
Linking options:
https://www.mathnet.ru/eng/timm1081 https://www.mathnet.ru/eng/timm/v20/i2/p311
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