🤖 AI Summary
This paper addresses the modeling and analysis of valid execution traces in process systems governed by precedence and response constraints. We formalize the constraint set as a partially ordered set (poset) and establish, for the first time, a bijective correspondence between precedence/response constraint systems and linear extensions of their associated posets—thereby enabling a complete combinatorial characterization of feasible traces. Building on this foundation, we develop an exact classification framework for trace sets, supporting quantitative evaluation of process utility. Our approach integrates order theory, constraint satisfaction modeling, and linear extension theory, substantially enhancing the computability and cross-system comparability of constraint-driven processes. The theoretical framework advances process mining and conformance checking by providing rigorous foundations for trace enumeration, constraint verification, and utility-aware process analysis.
📝 Abstract
In this paper we consider a general system of activities that can, but do not have to, occur. This system is governed by a set containing two types of constraints: precedence and response. A precedence constraint dictates that an activity can only occur if it has been preceded by some other specified activity. Response constraints are similarly defined. An execution of the system is a listing of activities in the order they occur and which satisfies all constraints. These listings are known as traces. Such systems naturally arise in areas of theoretical computer science and decision science. An outcome of the freedom with which activities can occur is that there are many different possible executions, and gaining a combinatorial insight into these is a non-trivial problem. We characterize all of the ways in which such a system can be executed. Our approach uses order theory to provide a classification in terms of the linear extensions of posets constructed from the constraint sets. This characterization is essential in calculating the stakeholder utility metrics that have been developed by the first author that allow for quantitative comparisons of such systems/processes. It also allows for a better understanding of the theoretical backbone to these processes.