α -algorithm is suitable to discover a large class of workflow (WF) nets based on the behaviour recorded in event logs, with the main limiting assumption that the event log is complete. Our research has been aimed at finding ways of discovering business process models based on examples of traces, ie, logs of workflow actions that do not meet the requirement of completeness. In this aim, we have modified the existing and introduced a new relation between activities recorded in the event log, which has led to a partial correction of the process models discovering technique, including the α -algorithm. We have also introduced the notion of causally complete logs, from which our modified algorithm can produce the same result as the α -algorithm from complete logs. The effect of these modifications on the efficiency of the process model discovering is mostly evident for business processes in which many activities can be performed in parallel. The application of the modified method for discovering block-structured models of parallel business processes is presented in this paper.K e y w o r d s: process mining, business process model discovery, block-structured parallel process models, complete log, α -algorithm

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Programming by demonstration (PBD) is a technique which allows end users to create, modify, accommodate, and expand programs by demonstrating what the program is supposed to do. Although the ideal of common-purpose programming by demonstration or by examples has been rejected as practically unrealistic, this approach has found its application and shown potentials when limited to specific narrow domains and ranges of applications. In this paper, the original method of applying the principles of programming by demonstration in the area of process mining (PM) to interactive construction of block-structured parallel business processes models is presented. A technique and tool that enable interactive process mining and incremental discovery of process models have been described in this paper. The idea is based on the following principle: using a demonstrational user interface, a user demonstrates scenarios of execution of parallel business process activities, and the system gives a generalized model process specification. A modified process mining technique with the α|| algorithm applied on weakly complete event logs is used for creating parallel business process models using demonstration.

It is known that meteorological variables from meteorological online services can be used for the design of photovoltaic (PV) water pumping systems for irrigation. The software LORENTZ COMPASS in such a manner uses as inputs solar irradiation, precipitation, and ambient temperature collected by the NASA Langley Research Centre over a period of more than 20 years. This paper proposes a novel procedure that uses the sunshine duration, precipitation, and ambient temperature as inputs. These inputs were collected by Weather Online UK during a period of 25 years. The effects of different data collection periods and data availabilities on the design of the PV water pumping system are also analysed and discussed. Along with the meteorological data, the proposed procedure uses as inputs datasheets from manufacturers of pumping systems and PV modules. The procedure is based on the Sivkov model that correlates the global horizontal irradiation with the sunshine duration and the elevation angle of the Sun. A case study, i.e., an existing PV water pumping system designed using LORENTZ COMPASS is used as reference for purposes of comparison and validation of the procedure. The results of the comparison showed a high level of accuracy, and a number of interesting conclusions are drawn from them.

Many information systems have a possibility to record their execution, and, in this way, to generate a trace about events describing the real system behaviour. From behaviour example records in traces of the event log, the α-algorithm automatically generates a process model that belongs to a subclass of Petri nets, known as workflow nets. One of the basic limiting assumptions of α-algorithm is that the event log needs to be complete. As a result of attempting to overcome the problem of completeness of the event log, we introduced the notion of weakly complete event logs, from which our modified technique and algorithm can produce the same result as the α-algorithm from complete logs on parallel processes. Thereby weakly complete logs can be significantly smaller than complete logs, considering the number of traces they consist of. Weakly complete logs were used for the realization of our idea of interactive parallel business process model generation.