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Tile transition systems as structured coalgebras?

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Fundamentals of Computation Theory (FCT 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1684))

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Abstract

The aim of this paper is to investigate the relation between two models of concurrent systems: tile rewrite systems and coalgebras. Tiles are rewrite rules with side eects which are endowed with operations of parallel and sequential composition and synchronization. Their models can be described as monoidal double categories. Coalgebras can be considered, in a suitable mathematical setting, as dual to algebras. They can be used as models of dynamical systems with hidden states in order to study concepts of observational equivalence and bisimilarity in a more general setting.

In order to capture in the coalgebraic presentation the algebraic structure given by the composition operations on tiles, coalgebras have to be endowed with an algebraic structure as well. This leads to the concept of structured coalgebras, i.e., coalgebras for an endofunctor on a category of algebras.

However, structured coalgebras are more restrictive than tile models. Those models which can be presented as structured coalgebras are characterized by the so-called horizontal decomposition property, which, intuitively, requires that the behavior is compositional in the sense that all transitions from complex states can be derived by composing transitions out of component states.

Article

Research partially supported by MURST project Tecniche Formali per Sistemi Software, by CNR Integrated Project Metodi per Sistemi Connessi mediante Reti, by TMR Network GETGRATS and by Esprit WGs APPLIGRAPH, CONFER2 and COORDINA.

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Universita degli Studi di Pisa, Corso Italia, 40, I - 56125, Pisa, Italia

    Andrea Corradini & Ugo Montanari

  2. Universität GH Paderborn, FB 17 Mathematik und Informatik, Warburger Str. 100, D-33098, Paderborn, Germany

    Reiko Heckel

Authors
  1. Andrea Corradini
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  2. Reiko Heckel
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  3. Ugo Montanari
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Editor information

Editors and Affiliations

  1. Faculty of Computer Science, “A.I.Cuza” University, 6600, Iaşi, Romania

    Gabriel Ciobanu

  2. Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 70700, Bucharest, Romania

    Gheorghe Păun

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Corradini, A., Heckel, R., Montanari, U. (1999). Tile transition systems as structured coalgebras?. In: Ciobanu, G., Păun, G. (eds) Fundamentals of Computation Theory. FCT 1999. Lecture Notes in Computer Science, vol 1684. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48321-7_2

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  • DOI: https://doi.org/10.1007/3-540-48321-7_2

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  • Print ISBN: 978-3-540-66412-3

  • Online ISBN: 978-3-540-48321-2

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