The following paper has been published in Information & Computation:
Posets With Interfaces as a Model for Concurrency
Uli Fahrenberg, Christian Johansen, Georg Struth, Krzysztof Ziemiański
We introduce posets with interfaces (iposets) and generalise their standard
serial composition to a new gluing composition. In the partial order
semantics of concurrency, interfaces and gluing allow modelling events that
extend in time and across components. Alternativelytaking a decompositional
view, interfaces allow cutting through events, while serial composition may
only cut through edges of a poset. We show that iposets under gluing
composition form a category, which generalises the monoid of posets under
serial composition up to isomorphism. They form a 2-category when a
subsumption order and a lax tensor in the form of a non-commutative parallel
composition are added, which generalises the interchange monoids used for
modelling series-parallel posets. We also study the gluing-parallel
hierarchy of iposets, which generalises the standard series-parallel one.
The class of gluing-parallel iposets contains that of series-parallel posets
and the class of interval orders, which are well studied in concurrency
theory, too. We also show that it is strictly contained in the class of all
iposets by identifying several forbidden substructures.
https://www.lrde.epita.fr/wiki/Publications/fahrenberg.22.iandc
