Processes and unfoldings: concurrent computations in adhesive categories

Paolo Baldan, Andrea Corradini, Tobias Heindel, Barbara König, Pawel Sobocinski

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
Number of pages40
JournalMathematical Structures in Computer Science
Volume24
Issue number4
DOIs
Publication statusPublished - 26 Jun 2014

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