A concrete realization of the Hoare powerdomain

Hart, James B.; Tsinakis, Constantine

doi:10.1007/s00500-007-0153-3

Cited by 4 publications

(4 citation statements)

References 9 publications

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“…Powerset Lattice. The powerset lattice that describes a Hoare powertheory [2,34,44]-over a given lattice…”

Section: Key Insightsmentioning

confidence: 99%

Abstract Transducers

Stahlbauer

2019

Preprint

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Several abstract machines that operate on symbolic input alphabets have been proposed in the last decade, for example, symbolic automata or lattice automata. Applications of these types of automata include software security analysis and natural language processing. While these models provide means to describe words over infinite input alphabets, there is no considerable work on symbolic output (as present in transducers) alphabets, or even abstraction (widening) thereof. Furthermore, established approaches for transforming, for example, minimizing or reducing, finite-state machines that produce output on states or transitions are not applicable. A notion of equivalence of this type of machines is needed to make statements about whether or not transformations maintain the semantics.We present abstract transducers as a new form of finite-state transducers. Both their input alphabet and the output alphabet is composed of abstract words, where one abstract word represents a set of concrete words. The mapping between these representations is described by abstract word domains. By using words instead of single letters, abstract transducers provide the possibility of lookaheads to decide on state transitions to conduct. Since both the input symbol and the output symbol on each transition is an abstract entity, abstraction techniques can be applied naturally.We apply abstract transducers as the foundation for sharing task artifacts for reuse in context of program analysis and verification, and describe task artifacts as abstract words. A task artifact is any entity that contributes to an analysis task and its solution, for example, candidate invariants or source code to weave.

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“…Powerset Lattice. The powerset lattice that describes a Hoare powertheory [2,34,44]-over a given lattice…”

Section: Key Insightsmentioning

confidence: 99%

Abstract Transducers

Stahlbauer

2019

Preprint

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“…The definition of an information system given in the previous section makes it possible to think of the consistency predicate as a preordered set; hence, it is natural to examine the pre-order convex substructures of this set. In Hart and Tsinakis [5], we show that the lower sets of the consistency predicate for an information system S correspond to so-called full subinformation systems of S and show that this family provides a concrete realization of the Hoare powerdomain of the domain corresponding to S. Since the Smyth preorder is, in a sense, the dual of the Hoare preorder, it is natural to think that the Smyth powerdomain for the domain corresponding to S may be realized concretely as some family of upper-sets of the consistency predicate. This turns out to be true, but upper-sets of the consistency predicate pose a semantic problem not encountered with lower sets -they do not correspond to any type of subinformation system in S. As we will show, partial information systems provide a way of understanding upper-sets in the consistency predicate as substructures of the information system.…”

Section: A Novel Representation Of the Smyth Powerdomainmentioning

confidence: 99%

“…Since it is possible to view information systems as preordered structures, it therefore seems reasonable to attempt representing order theoretic entities well-known to computer science in terms of order-convex subobjects of information systems, especially when these subobjects can be given a natural semantic interpretation. In Hart and Tsinakis [5], we prove that the Hoare powerdomain can be represented in such a way. The current paper continues this theme by showing it is possible to identify the Smyth powerdomain with a family of order-convex subobjects in a structure closely related to information systems.…”

Section: Introductionmentioning

confidence: 99%

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Partial information systems and the Smyth powerdomain

Hart

2012

Mathematica Slovaca

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ABSTRACT. The dual of the join semilattice of proper compact Scott open subsets of a domain D is called the Smyth powerdomain of D. The Smyth powerdomain is used in programming semantics as a model for demonic nondeterminism. In this paper, we introduce the concept of partial information systems; and, as an application, show that the Smyth powerdomain of any domain can be realized in terms of the sub partial information systems of the domain's corresponding information system.

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Ordinal decompositions for preordered root systems

Hart

Tsinakis

2009

Annals of Pure and Applied Logic

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a b s t r a c tIn this paper, we explore the effects of certain forbidden substructure conditions on preordered sets. In particular, we characterize in terms of these conditions those preordered sets which can be represented as the supremum of a well-ordered ascending chain of lowersets whose members are constructed by means of alternating applications of disjoint union and ordinal sums with chains. These decompositions are examples of ordinal decompositions in relatively normal lattices as introduced by Snodgrass, Tsinakis, and Hart. We conclude the paper with an application to information systems.

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A concrete realization of the Hoare powerdomain

Cited by 4 publications

References 9 publications

Abstract Transducers

Abstract Transducers

Partial information systems and the Smyth powerdomain

Ordinal decompositions for preordered root systems

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