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Weighted Relational Models for Mobility

Author James Laird

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James Laird

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James Laird. Weighted Relational Models for Mobility. In 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 52, pp. 24:1-24:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.FSCD.2016.24

Abstract

We investigate operational and denotational semantics for
computational and concurrent systems with mobile names which capture
their computational properties.  For example, various properties of
fixed networks, such as shortest or longest path, transition
probabilities, and secure data flows, correspond to the ``sum'' in a
semiring of the weights of paths through the network: we aim to model
networks with a dynamic topology in a similar way. Alongside rich
computational formalisms such as the lambda-calculus, these can be
represented as terms in a calculus of solos with weights from a
complete semiring $R$, so that reduction associates a weight in R to
each reduction path.

Taking inspiration from differential nets, we develop a denotational
semantics for this calculus in the category of sets and R-weighted
relations, based on its differential and compact-closed structure, but
giving a simple, syntax-independent representation of terms as
matrices over R. We show that this corresponds to the sum in R of
the values associated to its independent reduction paths, and that our
semantics is fully abstract with respect to the observational
equivalence induced by sum-of-paths evaluation.

Subject Classification

Keywords
  • Concurrency
  • Mobility
  • Denotational Semantics

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