Logic and Algebra in Unfolded Petri Nets: on a Duality Between Concurrency and Causal Dependence

Autor:	Lucia Pomello, Luca Bernardinello, Carlo Ferigato
Přispěvatelé:	Bernardinello, L, Ferigato, C, Pomello, L
Rok vydání:	2019
Předmět:	Algebra Algebra and Number Theory Computational Theory and Mathematics Concurrency INF/01 - INFORMATICA Duality (optimization) Algebra over a field Petri net Concurrency Orthogonality relations Causal Dependence relation Petri nets Information Systems Theoretical Computer Science Mathematics
Zdroj:	Fundamenta Informaticae. 171:39-56
ISSN:	1875-8681 0169-2968
Popis:	An orthogonality space is a set endowed with a symmetric and irreflexive binary relation (an orthogonality relation). In a partially ordered set modelling a concurrent process, two such binary relations can be defined: a causal dependence relation and a concurrency relation, and two distinct orthogonality spaces are consequently obtained. When the condition of N-density holds on both these orthogonality spaces, we study the orthomodular poset formed by closed sets defined according to Dacey. We show that the condition originally imposed by Dacey on the orthogonality spaces for obtaining an orthomodular poset from his closed sets is in fact equivalent to N-density. The requirement of N-density was as well fundamental in a previous work on orthogonality spaces with the concurrency relation. Starting from a partially ordered set modelling a concurrent process, we obtain dual results for orthogonality spaces with the causal dependence relation in respect to orthogonality spaces with the concurrency relation.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c4d17455e68e4739c9600a878e33ce75 https://doi.org/10.3233/fi-2020-1871 Zobrazit plný text záznamu