Regular orthomodular posets

Andrzej Borzyszkowski

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.
Author Andrzej Borzyszkowski (FMPI / II)
Andrzej Borzyszkowski,,
- Institute of Informatics
Journal seriesFundamenta Informaticae, ISSN 0169-2968, e-ISSN 1875-8681, (N/A 70 pkt)
Issue year2019
Vol166
No1
Pages15-28
Publication size in sheets0.65
Keywords in Englishorthomodular poset, 2-structure, theory of regions, concurrency theory
ASJC Classification1703 Computational Theory and Mathematics; 1710 Information Systems; 2602 Algebra and Number Theory; 2614 Theoretical Computer Science
DOIDOI:10.3233/FI-2019-1792
Languageen angielski
Score (nominal)70
Score sourcejournalList
ScoreMinisterial score = 70.0, 28-01-2020, ArticleFromJournal
Publication indicators WoS Citations = 0; Scopus SNIP (Source Normalised Impact per Paper): 2018 = 0.821; WoS Impact Factor: 2018 = 1.204 (2) - 2018=0.83 (5)
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