منابع مشابه
Invariant Relations: An Alternative Tool to Analyze Loops
Since their introduction more than four decades ago, invariant assertions have, justifiably, dominated the analysis of while loops, and have been the focus of sustained research interest in the seventies and eighties, and renewed interest in the last decade. In this paper, we tentatively submit an alternative concept for the analysis of while loops, explore its attributes, and its relationship ...
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Let $mathcal{A}$ be a unital Banach algebra, $mathcal{M}$ be a left $mathcal{A}$-module, and $W$ in $mathcal{Z}(mathcal{A})$ be a left separating point of $mathcal{M}$. We show that if $mathcal{M}$ is a unital left $mathcal{A}$-module and $delta$ is a linear mapping from $mathcal{A}$ into $mathcal{M}$, then the following four conditions are equivalent: (i) $delta$ is a Jordan left de...
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A loop Q is said to be left conjugacy closed (LCC) if the left translations form a set of permutations that is closed under conjugation. Loops in which the left and right nuclei coincide and are of index 2 are necesarilly LCC, and they are constructed in the paper explicitly. LCC loops Q with the right nucleus G of index 2 offer a larger diversity. A sample of results: if Z(G) = 1, then Q is al...
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In a series of papers from the 1940’s and 1950’s, R.H. Bruck and L.J. Paige developed a provocative line of research detailing the similarities between two important classes of loops: the diassociative A-loops and the Moufang loops ([1]). Though they did not publish any classification theorems, in 1958, Bruck’s colleague, J.M. Osborn, managed to show that diassociative, commutative A-loops are ...
متن کاملLecture Notes on Invariants for While Loops and Arbitrary Loops
The previous lecture provided axioms for compositional reasoning about deterministic sequential programs. All the axioms compositionally reduce the truth of a postcondition of a more complex program to a logical combination of postconditions of simpler programs. All axioms? Well, all the axioms but one: those about loops. But putting loops aside for the moment, these axioms completely tell us w...
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ژورنال
عنوان ژورنال: Matrix Science Mathematic
سال: 2017
ISSN: 2521-0831,2521-084X
DOI: 10.26480/msmk.02.2017.04.05