Toward a Uniform Approach to the Unfolding of Nets

Abstract

In this paper we introduce the notion of spread net. Spread nets are (safe) Petri nets equipped with vector clocks on places and with ticking functions on transitions, and are such that vector clocks are consistent with the ticking of transitions. Such nets generalize previous families of nets like unfoldings, merged processes and trellis processes, and can thus be used to represent runs of a net in a true concurrency semantics through an operation called the spreading of a net. By contrast with previous constructions, which may identify conflicts, spread nets allow loops in time.

Spreading nets: A uniform approach to unfoldings

“…In this way it is possible to keep track of the way that place is reached (obtained) in the executions represented by that net. Based on this notion, we continue the line of research initiated in [17] for multi-clock nets, and we show how the notion of spreading of nets can be seen as a unified approach to Petri net unfolding, also for nets that are not multi-clock nets. While trellises and merged processes had abandoned the requirement that nodes should not be in self-conflict in the unfolding, the main move here is to abandon also the requirement that the unfolding should be a (directed) acyclic graph.…”

“…This paper is a revised and extended version of [17]. Whereas in [17] only multi-clock nets were considered, here we generalize the notion of spread net to any kind of net. More importantly we show that classical unfoldings can be seen as spread nets, by constructing adequate information domains.…”

“…Spread nets ( [17]) are nets where each place is annotated, and the annotation depends on the transitions putting a token in that place and on the annotations of the places feeding these transitions. In this way it is possible to keep track of the way that place is reached (obtained) in the executions represented by that net.…”

Operational Representation of Dependencies in Context-Dependent Event Structures

“…Most of the approaches relating nets with event structures are based on the equation "event = transition", even if many of the events represent the same high level activity. The idea that some of the transitions may be somehow identified as they represent the same activity is the one pursued in many works aiming at reducing the size of the net, like merged processes ( [KKKV06]), trellis processes ( [Fab07]), merging relation approach ( [CP17a]) or spread nets ( [FP18] and [PF20]), but these approaches are mostly unrelated with event structure of any kind.…”