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Software Verification and System Assurance
, 2009
"... Littlewood [1] introduced the idea that software may be possibly perfect and that we can contemplate its probability of (im)perfection. We review this idea and show how it provides a bridge between correctness, which is the goal of software verification (and especially formal verification), and the ..."
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Cited by 7 (2 self)
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Littlewood [1] introduced the idea that software may be possibly perfect and that we can contemplate its probability of (im)perfection. We review this idea and show how it provides a bridge between correctness, which is the goal of software verification (and especially formal verification), and the probabilistic properties such as reliability that are the targets for systemlevel assurance. We enumerate the hazards to formal verification, consider how each of these may be countered, and propose relative weightings that an assessor may employ in assigning a probability of perfection.
Efficient Rough Set Theory Merging
"... Abstract. Theory exploration is a term describing the development of a formal (i.e. with the help of an automated proofassistant) approach to selected topic, usually within mathematics or computer science. This activityhoweverusuallydoesn’t reflecttheviewofscience consideredasa whole, notas separat ..."
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Abstract. Theory exploration is a term describing the development of a formal (i.e. with the help of an automated proofassistant) approach to selected topic, usually within mathematics or computer science. This activityhoweverusuallydoesn’t reflecttheviewofscience consideredasa whole, notas separated islands ofknowledge. Merging theoriesessentially has its primary aim of bridging these gaps between specific disciplines. As we provided formal apparatus for basic notions within rough set theory (as e.g. approximation operators and membership functions), we try to reuse the knowledge which is already contained in available repositories of computerchecked mathematical knowledge, or which can be obtained in a relatively easy way. We can point out at least three topics here: topological aspects of rough sets – as approximation operators have properties of the topological interior and closure; latticetheoretic approach giving the algebraic viewpoint (e.g. Stone algebras); possible connections with formal concept analysis. In such a way we can give the formal characterization of rough sets in terms of topologies or orders. Although fully formal, still the approach can be revised to keep the uniformity all the time.