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Processes and unfoldings: concurrent computations in adhesive categories

Published online by Cambridge University Press:  26 June 2014

PAOLO BALDAN ,
ANDREA CORRADINI ,
TOBIAS HEINDEL ,
BARBARA KÖNIG  and
PAWEŁ SOBOCIŃSKI
PAOLO BALDAN
Affiliation:
Dipartimento di Matematica Pura e Applicata, Università di Padova, Italy Email: baldan@math.unipd.it
ANDREA CORRADINI
Affiliation:
Dipartimento di Informatica, Università di Pisa, Italy Email: andrea@di.unipi.it
TOBIAS HEINDEL
Affiliation:
School of Informatics, University of Edinburgh, Edinburgh, United Kingdom Email: tobias.heindel@googlemail.com
BARBARA KÖNIG
Affiliation:
Abteilung für Informatik und Angewandte Kognitionswissenschaft, Universität Duisburg-Essen, Germany Email: barbara_koenig@uni-due.de
PAWEŁ SOBOCIŃSKI
Affiliation:
ECS, University of Southampton, United Kingdom Email: ps@ecs.soton.ac.uk
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Abstract

We generalise both the notion of a non-sequential process and the unfolding construction (which was previously developed for concrete formalisms such as Petri nets and graph grammars) to the abstract setting of (single pushout) rewriting of objects in adhesive categories. The main results show that processes are in one-to-one correspondence with switch-equivalent classes of derivations, and that the unfolding construction can be characterised as a coreflection, that is, the unfolding functor arises as the right adjoint to the embedding of the category of occurrence grammars into the category of grammars.

As the unfolding represents potentially infinite computations, we need to work in adhesive categories with ‘well-behaved’ colimits of ω-chains of monos. Compared with previous work on the unfolding of Petri nets and graph grammars, our results apply to a wider class of systems, which is due to the use of a refined notion of grammar morphism.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 24 , Issue 4: Structure Transformation , August 2014 , 240402
Copyright
Copyright © Cambridge University Press 2014 

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