Canonizable Partial Order Generators

In a previous work we introduced slice graphs as a way to specify both infinite languages of directed acyclic graphs (DAGs) and infinite languages of partial orders. Therein we focused on the study of Hasse diagram generators, i.e., slice graphs that generate only transitive reduced DAGs. In this work we prove that any slice graph SG can be effectively transformed into a Hasse diagram generator HG representing the same set of partial orders. Thus from an algorithmic standpoint we introduce a method of transitive reducing infinite families of DAGs specified by slice graphs. This result allows us to establish unknown connections between the true concurrent behavior of bounded p/t-nets and traditional approaches of representing infinite families of partial orders, such as Mazurkiewicz trace languages and message sequence chart (MSC) languages. For instance, given a partial order language LP O represented by a finite automaton A together with a Mazurkievicz independence alphabet (, I), an...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Mateus de Oliveira Oliveira
• Keywords: CORR 2010, Education, Hasse Diagram Generators, Partial Order, Slice Graphs