Binary Multirelations
نویسندگان
چکیده
Binary multirelations associate elements of a set with its subsets; hence they are binary relations of type A × 2. Applications include alternating automata, models and logics for games, program semantics with dual demonic and angelic nondeterministic choices and concurrent dynamic logics. This proof document supports an arXiv article that formalises the basic algebra of multirelations and proposes axiom systems for them, ranging from weak bi-monoids to weak bi-quantales.
منابع مشابه
UTP Designs for Binary Multirelations
The total correctness of sequential computations can be established through different isomorphic models, such as monotonic predicate transformers and binary multirelations, where both angelic and demonic nondeterminism are captured. Assertional models can also be used to characterise process algebras: in Hoare and He’s Unifying Theories of Programming, CSP processes can be specified as the rang...
متن کاملKleisli, Parikh and Peleg compositions and liftings for multirelations
Multirelations provide a semantic domain for computing systems that involve two dual kinds of nondeterminism. This paper presents relational formalisations of Kleisli, Parikh and Peleg compositions and liftings of multirelations. These liftings are similar to those that arise in the Kleisli category of the powerset monad. We show that Kleisli composition of multirelations is associative, but ne...
متن کاملMultirelations with infinite computations
Multirelations model computations with both angelic and demonic non-determinism. We extend multirelations to represent finite and infinite computations independently. We derive an approximation order for multirelations assuming only that the endless loop is its least element and that the lattice operations are isotone. We use relations, relation algebra and RelView for representing and calculat...
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We study operations and equational properties of multirelations, which have been used for modelling games, protocols, computations, contact, closure and topology. The operations and properties are expressed using sets, heterogeneous relation algebras and more general algebras for multirelations. We investigate the algebraic properties of a new composition operation based on the correspondence t...
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The correspondence between up-closed multirelations and isotone predicate transformers is well known. Less known is that multirelations have also been used for modelling topological contact, not only computations. We investigate how properties from these two lines of research translate to predicate transformers. To this end, we express the correspondence of multirelations and predicate transfor...
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عنوان ژورنال:
- Archive of Formal Proofs
دوره 2015 شماره
صفحات -
تاریخ انتشار 2015