Affiliations: Institute of Informatics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, Gdańsk, Poland. [email protected]
Correspondence:
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Address for correspondence: University of Gdańsk, Institute of Informatics, Faculty of Mathematics, Physics and Informatics, Wita Stwosza 57, 80-308 Gdańsk, Poland.
Abstract: Rozenberg and Ehrenfeucht has shown a duality between 2-structures (a.k.a. transition systems) and (elementary) Petri nets. The tool has been the notion of a region of a 2-structure, the regions then define a Petri net. Bernardinello et al. has observed that the regions of a 2-structure form an orthomodular poset and there is a similar relation between 2-structures and orthomodular posets. While in the theory of 2-structures we may ask if a 2-structure is full and forward closed, the analogous notion for orthomodular posets is their regularity. In the present paper we study the problem of closing a given orthomodular poset to a regular one. This is a dual problem to closing a 2-structure, which has been studied by the author earlier. Also, as in a seminal work of Rozenberg and Ehrenfeucht, one can be interested in a concrete representation, i.e. as a family of sets. We show here an appropriate construction for orthomodular posets too.
Keywords: orthomodular poset, 2-structure, theory of regions, concurrency theory
