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On the Expressive Power of Non-deterministic and Unambiguous Petri Nets over Infinite Words

Finkel Olivier, Skrzypczak Michał

Fundamenta Informaticae

2021

Vol. 183, nr 3-4

243--291

To identify the causes of performance problems or to predict process behavior, it is essential to have correct and complete event data. This is particularly important for distributed systems with shared resources, e.g., one case can block another case competing for the same machine, leading to inter-case dependencies in performance. However, due to a variety of reasons, real-life systems often record only a subset of all events taking place. To understand and analyze the behavior and performance of processes with shared resources, we aim to reconstruct bounds for timestamps of events in a case that must have happened but were not recorded by inference over events in other cases in the system. We formulate and solve the problem by systematically introducing multi-entity concepts in event logs and process models. We introduce a partial-order based model of a multi-entity event log and a corresponding compositional model for multi-entity processes. We define PQR-systems as a special class of multi-entity processes with shared resources and queues. We then study the problem of inferring from an incomplete event log unobserved events and their timestamps that are globally consistent with a PQR-system. We solve the problem by reconstructing unobserved traces of resources and queues according to the PQR-model and derive bounds for their timestamps using a linear program. While the problem is illustrated for material handling systems like baggage handling systems in airports, the approach can be applied to other settings where recording is incomplete. The ideas have been implemented in ProM and were evaluated using both synthetic and real-life event logs.

Deterministic and Unambiguous Families within Recognizable Two-dimensional Languages

Anselmo M., Giammarresi D., Madonia M.

Fundamenta Informaticae

2010

Vol. 98, nr 2/3

143-166

Recognizable two-dimensional languages (REC) are defined by tiling systems that generalize to two dimensions non-deterministic finite automata for strings. We introduce the notion of deterministic tiling system and the corresponding family of languages (DREC) and study its structural and closure properties. Furthermore we show that, in contrast with the one-dimensional case, there exist other classes between deterministic and non-deterministic families that we separate by means of examples and decidability properties.