Regular Orthomodular Posets

• Autorzy: Borzyszkowski Andrzej M.

Identyfikatory

DOI

10.3233/FI-2019-1792

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

orthomodular poset; 2-structure; theory of regions; concurrency theory

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2019
• Tom: Vol. 166, nr 1
• Strony: 15--28
• Opis fizyczny: Bibliogr. 6 poz., rys.

Twórcy

autor

Borzyszkowski Andrzej M.

• Institute of Informatics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, Gdańsk, Poland

Bibliografia

• [1] Bernardinello L, Ferigato C, Pomello L. An Algebraic Model of Observable Properties in Distributed Systems. Theoretical Computer Science, 2003;290:637-668. doi:10.1016/S0304-3975(02)00046-4.
• [2] Ehrenfeucht A, Rozenberg G. Partial (Set) 2-structures, part I. Acta Informatica, 1990;27(4):315-342. doi:10.1007/BF00264611.
• [3] Badouel E, Bernardinello L, Darondeau P. Petri Net Synthesis. Springer, Berlin Heidelberg, 2015; ISBN:978-3-662-47966-7, 978-3-662-51621-8.
• [4] Birkhoff G, von Neumann J. The Logic of Quantum Mechanics. Ann. of Math., 1936;37(4):823-843. doi:10.2307/1968621.
• [5] Bernardinello L, Pomello L, Rombolà S. On Orthomodular Posets Generated by Transition Systems. Electronic Notes in TCS, 2011;270(1):147-154. doi:10.1016/j.entcs.2011.01.013.
• [6] Dvurečenskij A, Pulmannová S. New Trends in Quantum Structures. Kluwer Academic Publishers, Dordrecht, 2000. doi:10.1007/978-94-017-2422-7.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).