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Unfolding grammars in adhesive categories

Unfolding grammars in adhesive categories
Unfolding grammars in adhesive categories
We generalize the unfolding semantics, previously developed for concrete formalisms such as Petri nets and graph grammars, to the abstract setting of (single pushout) rewriting over adhesive categories. The unfolding construction is characterized 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 towork in adhesive categories with “well-behaved” colimits of ω-chains of monomorphisms. Compared to previous work on the unfolding of Petrinets 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.
350-366
Baldan, Paolo
327d96b7-f7a3-4f5b-835b-0a7cbc825f73
Corradini, Andrea
6cc7a106-fbf7-459c-90ae-bc855c67c664
Heindel, Tobias
b9fb4c42-8552-4f9b-933f-ce41dcbee2ac
König, Barbara
58102e16-713c-4f0e-9ea6-57063c8ca13b
Sobociński, Paweł
439334ab-2826-447b-9fe5-3928be3fd4fd
Kurz, Alexander
685abe8c-fd80-4a3a-8c12-356d85738fc6
Lenisa, Marina
a19eb625-2209-4a24-91c7-e0c4e8c39a0e
Tarlecki, Andrzej
c4692648-f6e6-4a4c-99c8-25acdcf2fba2
Baldan, Paolo
327d96b7-f7a3-4f5b-835b-0a7cbc825f73
Corradini, Andrea
6cc7a106-fbf7-459c-90ae-bc855c67c664
Heindel, Tobias
b9fb4c42-8552-4f9b-933f-ce41dcbee2ac
König, Barbara
58102e16-713c-4f0e-9ea6-57063c8ca13b
Sobociński, Paweł
439334ab-2826-447b-9fe5-3928be3fd4fd
Kurz, Alexander
685abe8c-fd80-4a3a-8c12-356d85738fc6
Lenisa, Marina
a19eb625-2209-4a24-91c7-e0c4e8c39a0e
Tarlecki, Andrzej
c4692648-f6e6-4a4c-99c8-25acdcf2fba2

Baldan, Paolo, Corradini, Andrea, Heindel, Tobias, König, Barbara and Sobociński, Paweł (2009) Unfolding grammars in adhesive categories. Kurz, Alexander, Lenisa, Marina and Tarlecki, Andrzej (eds.) 3rd Conference on Algebra and Coalgebra in Computer Science (CALCO '09), Udine, Italy. 07 - 10 Sep 2009. pp. 350-366 .

Record type: Conference or Workshop Item (Paper)

Abstract

We generalize the unfolding semantics, previously developed for concrete formalisms such as Petri nets and graph grammars, to the abstract setting of (single pushout) rewriting over adhesive categories. The unfolding construction is characterized 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 towork in adhesive categories with “well-behaved” colimits of ω-chains of monomorphisms. Compared to previous work on the unfolding of Petrinets 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

Published date: September 2009
Additional Information: Event Dates: September 7-10, 2009
Venue - Dates: 3rd Conference on Algebra and Coalgebra in Computer Science (CALCO '09), Udine, Italy, 2009-09-07 - 2009-09-10

Identifiers

Local EPrints ID: 188455
URI: http://eprints.soton.ac.uk/id/eprint/188455
PURE UUID: 03a1d8c3-0baf-4d0c-90c3-511885e0fbbd

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Date deposited: 25 May 2011 10:15
Last modified: 03 Dec 2019 17:31

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