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Abstract
We are interested in the relation between weak and strong temporal operators. We would like to find a characterization that shows what it means for an operator to be the weak or strong version of another operator, or more generally for a formula to be a weak or strong version of another formula. We show that the weak version of a formula is not the same as Alpern and Schneider's safety component. By working over an extended alphabet, we show that their topological characterization of safety can be adapted to obtain a topological characterization of weakness. We study the resulting topology and the relations between weak and strong formulas. Finally, we apply the method to show the internal consistency of a logic containing both weak and strong versions of regular expressions.
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Cite it as
@misc{eisner2005topological,
title = {A topological characterization of weakness},
author = {Cindy Eisner and Dana Fisman and John Havlicek},
year = {2005},
journal = {ACM Symposium on Principles of Distributed Computing (PODC)},
pages = {1--8},
doi = {10.1145/1073814.1073816},
}