Simulations in coalgebra

  • Authors:

  • Jesse Hughes;Bart Jacobs

  • Affiliations:

  • Department of Philosophy, Technical University of Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands and Department of Philosophy, Technical University of Eindhoven, P.O. Box 9010, Eindho ...;Department of Computer Science, University of Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands

  • Venue:
  • Theoretical Computer Science - Selected papers of CMCS'03
  • Year:
  • 2004

Quantified Score

Hi-index 0.00

Visualization

Abstract

A new approach to simulations is proposed within the theory of coalgebras by taking a notion of order on a functor as primitive. Such an order forms a basic building block for a "lax relation lifting", or "relator" as used by other authors. Simulations appear as coalgebras of this lifted functor, and similarity as greatest simulation. Two-way similarity is then similarity in both directions. In general, it is different from bisimilarity (in the usual coalgebraic sense), but a sufficient condition is formulated (and illustrated) to ensure that bisimilarity and two-way similarity coincide. Also, suitable conditions are identified which ensures that similarity on a final coalgebra forms an (algebraic) dcpo structure. This involves a close investigation of the iterated applications Fn(0) and Fn(1) of a functor F with an order to the initial algebras and final objects.