A Fixpoint-Based Calculus for Graph-Shaped Computational Fields

  • Alberto Lluch LafuenteEmail author
  • Michele Loreti
  • Ugo Montanari
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9037)


Coordination is essential for dynamic distributed systems exhibiting autonomous behaviors. Spatially distributed, locally interacting, propagating computational fields are particularly appealing for allowing components to join and leave with little or no overhead. In our approach, the space topology is represented by a graph-shaped field, namely a network with attributes on both nodes and arcs, where arcs represent interaction capabilities between nodes. We propose a calculus where computation is strictly synchronous and corresponds to sequential computations of fixpoints in the graph-shaped field. Under some conditions, those fixpoints can be computed by synchronised iterations, where in each iteration the attributes of a node is updated based on the attributes of the neighbours in the previous iteration. Basic constructs are reminiscent of the semiring μ-calculus, a semiring-valued generalisation of the modal μ-calculus, which provides a flexible mechanism to specify the neighbourhood range (according to path formulae) and the way attributes should be combined (through semiring operators). Additional control-flow constructs allow one to conveniently structure the fixpoint computations. We illustrate our approach with a case study based on a disaster recovery scenario, implemented in a prototype simulator that we use to evaluate the performance of a disaster recovery strategy.


Span Tree Distribute Hash Table Edge Label Disaster Recovery Tuple Space 
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Copyright information

© IFIP International Federation for Information Processing 2015

Authors and Affiliations

  • Alberto Lluch Lafuente
    • 1
    Email author
  • Michele Loreti
    • 2
  • Ugo Montanari
    • 3
  1. 1.DTU ComputeTechnical University of DenmarkKgs. LyngbyDenmark
  2. 2.University of FlorenceFirenzeItaly
  3. 3.Computer Science DepartmentUniversity of PisaPisaItaly

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