Families of Symmetries as Efficient Models of Resource Binding

Authors

Vincenzo Ciancia, Institute for Logic, Language and Computation - Amsterdam
Alexander Kurz, Chapman UniversityFollow
Ugo Montanari, Università di Pisa

Document Type

Article

Publication Date

2010

Abstract

Calculi that feature resource-allocating constructs (e.g. the pi-calculus or the fusion calculus) require special kinds of models. The best-known ones are presheaves and nominal sets. But named sets have the advantage of being finite in a wide range of cases where the other two are infinite. The three models are equivalent. Finiteness of named sets is strictly related to the notion of finite support in nominal sets and the corresponding presheaves. We show that named sets are generalisd by the categorical model of families, that is, free coproduct completions, indexed by symmetries, and explain how locality of interfaces gives good computational properties to families. We generalise previous equivalence results by introducing a notion of minimal support in presheaf categories indexed over small categories of monos. Functors and categories of coalgebras may be defined over families. We show that the final coalgebra has the greatest possible symmetry up-to bisimilarity, which can be computed by iteration along the terminal sequence, thanks to finiteness of the representation.

Comments

This article was originally published in Electronic Notes in Theoretical Computer Science, volume 264, issue 2, in 2010. DOI: 10.1016/j.entcs.2010.07.014

Recommended Citation

V. Ciancia, A. Kurz, and U. Montanari, “Families of Symmetries as Efficient Models of Resource Binding,” Electronic Notes in Theoretical Computer Science, vol. 264, no. 2, pp. 63–81, Aug. 2010. DOI: 10.1016/j.entcs.2010.07.014

Copyright

Elsevier

Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.