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Processes and unfoldings: concurrent computations in adhesive categories

Processes and unfoldings: concurrent computations in adhesive categories
Processes and unfoldings: concurrent computations in adhesive categories
We generalise both the notion of non-sequential process and the unfolding construction (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, i.e., 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 omega-chains of monos. Compared to 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.
1-40
Paolo, Baldan
524c3406-f5fa-4377-a1fb-41b95d056bef
Andrea, Corradini
fb56b628-ccad-48e7-9b33-8ed7b8c5eba1
Tobias, Heindel
fda2188c-0a9e-4dbd-ab71-16fccf4fbbb4
Barbara, Koenig
aeac22ac-7b87-45c5-891a-c618ee400254
Pawel, Sobocinski
439334ab-2826-447b-9fe5-3928be3fd4fd
Paolo, Baldan
524c3406-f5fa-4377-a1fb-41b95d056bef
Andrea, Corradini
fb56b628-ccad-48e7-9b33-8ed7b8c5eba1
Tobias, Heindel
fda2188c-0a9e-4dbd-ab71-16fccf4fbbb4
Barbara, Koenig
aeac22ac-7b87-45c5-891a-c618ee400254
Pawel, Sobocinski
439334ab-2826-447b-9fe5-3928be3fd4fd

Paolo, Baldan, Andrea, Corradini, Tobias, Heindel, Barbara, Koenig and Pawel, Sobocinski (2012) Processes and unfoldings: concurrent computations in adhesive categories. Mathematical Structures in Computer Science, 1-40.

Record type: Article

Abstract

We generalise both the notion of non-sequential process and the unfolding construction (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, i.e., 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 omega-chains of monos. Compared to 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.

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More information

Accepted/In Press date: January 2012
Published date: 2012
Organisations: Electronic & Software Systems

Identifiers

Local EPrints ID: 339066
URI: https://eprints.soton.ac.uk/id/eprint/339066
PURE UUID: 6dc2e699-b7ac-406b-bca0-1f341a943daf

Catalogue record

Date deposited: 22 May 2012 09:32
Last modified: 18 Jul 2017 05:55

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Contributors

Author: Baldan Paolo
Author: Corradini Andrea
Author: Heindel Tobias
Author: Koenig Barbara
Author: Sobocinski Pawel

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