Using process mining techniques, business analysts can find inefficiencies in business processes, with the ultimate aim of improving them. For efficient use of process improvement resources, it is important to recognise whether certain to-be-improved behaviour is frequent or rare. Such frequency information is referred to as the stochastic perspective in process mining, and techniques that take this stochastic information into account explicitly are called stochastic process mining techniques.

Stochastic process mining techniques are scattered across several process mining frameworks, such as Pm4py [1], BupaR [2] and ProM [3], each with its strengths and weaknesses, ranging from computational efficiency to ease of applicability in high-performance computing settings.

None of these existing frameworks (i) allows a straightforward application of a particular technique to an input file, (ii) none is easily accessible from the command line, (iii) all require installation and external runtime environments and, most importantly, (iv) none support exact computations throughout.

Ebi is a command line utility focused on stochastic process mining techniques. For end users, it allows direct application of stochastic process mining techniques to files, and writes the output to a file. No need to import, click through options and export, or even to write scripts. In particular, Ebi supports exact computations, which are a necessity in stochastic process mining (see Section 2).

For developers, Ebi is a framework that allows abstractions on inputs through interfaces ("traits"), such that implemented techniques automatically support a variety of input and output types. Furthermore, Ebi provides the means to perform exact computations easily, through custom implementations of corresponding data structures and methods such as matrix computations, as well as solvers and optimisation routines. Ebi as a framework ensures a consistent parameter handling, and is thus well positioned to act as a background library for Pm4py, BupaR and ProM in the future. Ebi is open source and we welcome contributions from the community.

The remainder of this paper is organised as follows. In Section 2, we discuss the significance of Ebi for stochastic process mining. Section 3 details its innovations. Section 4 lists the currently implemented techniques, while Section 5 discusses its maturity and Section 6 concludes the paper.

In stochastic process mining, techniques may need to deal with astonishingly small numbers. For instance, the BPIC11 [4] log has traces with more than 1 800 events. In any reasonable stochastic process model, the probability of such a trace would be well below 10 −300 , which is the minimum value that a double precision float can represent. Even if we could represent such low values reliably, doing any kind of computation would yield a low precision. For instance, if we want to compute the unit Earth-movers' stochastic conformance measure [5], we need to sum over one such value for each trace in the log, which would, in a typical log with thousands of traces, not leave any precision. In practice, computations on such logs without exact arithmetic would be highly unreliable. More numerically complex techniques that for instance require matrix computations like solving, inversion or multiplication with such low values would fare even worse. Hence, exact computations are a necessity in stochastic process mining, and Ebi is the first process mining framework that provides exact arithmetic for stochastic process mining.

Furthermore, having a command line interface eases the application of stochastic process mining techniques in demanding scientific experimental settings. Ebi is fully command-line based; though integrations with existing process mining frameworks such as Pm4py [1], BupaR [2] and ProM [3] are planned, in a similar fashion to Rust4pm [6].

Finally, Ebi encourages techniques to accept a large variety of inputs and produce a large variety of outputs, as it moves the burden of matching inputs and outputs of techniques to file types in the framework itself: by means of abstract interfaces (such as "a stochastic language that we can iterate over, and that iteration will end"), file types implement interfaces while techniques use them.

Ebi aims to provide stochastic process mining techniques to analysts in a consistent and coherent fashion, accessible through the command line. The Ebi framework provides the following innovations:

Ebi is a command line tool, which allows it to be applied easily in scientific experiment workflows. However, due to its structured set-up, it is well suited to be used as well as a fast background library for graphical tools or scripting languages such as Pm4py [1], BupaR [2] and ProM [3].

As described in Section 2, exact computations are a necessity in stochastic process mining.

Completely transparent to end users and techniques, Ebi uses fractions of unlimited size, explicit logarithms and explicit roots to perform almost all computations exactly. However, exact computations can be disabled by the user for performance reasons. For more details, please refer to the manual. Unfortunately, most existing Rust libraries do not accept unlimited fractions as input, let alone explicit representations of logarithms and roots. Therefore, many secondary techniques, such as linear solvers, matrix computations and approximation techniques, were adapted to support exact computations.

Completely transparent for end users, an implemented technique that needs to e.g. walk over the traces of an event log will automatically support all input formats for which that can be done. That is, techniques preferably define their inputs in terms of interfaces ("traits"). Again completely transparent to end users and techniques, the output of a technique is converted automatically by Ebi based on the file extension of the desired output file. For more details, please refer to the manual.

Ebi runs locally and neither needs nor uses internet access, which makes it suitable for privacy-sensitive settings. Use of the Rust programming language ensures most types of memory-related errors are absent. Furthermore, Rust is, of course dependent on the programmer, more energy efficient than Java and much more energy efficient than Python [7].

In Ebi, a command is the implementation of an algorithm. As summarised in Figure 1, a command defines the inputs it needs, in terms of traits and object types, as well its output type, in terms of an object type it will produce. For instance, the command will extract the most likely traces from its input. These inputs are (i) something that implements the FiniteStochasticLanguage or StochasticDeterministicSemantics trait, and (ii) an integer. When the user issues a command, Ebi will establish which traits and object types can serve as an input for the given command. For each of these traits and object types, Ebi will search which file handlers can provide it. For our example, the file handlers that can provide a usable input are a finite stochastic language (.slang), a compressed event log (.xes.gz), a stochastic labelled Petri net (.slpn), a stochastic deterministic finite automaton (.sdfa) and an event log (.xes). Ebi will attempt to load the given file with all of these file handlers, until it finds one that parses. Then, the command is executed. The command will result in an output, that is, an object of a particular object type. Then, Ebi will consider the file extension of the file the user wishes to write the result to, and see whether there is a file handler with that extension that can export the output object type. The main techniques for which Ebi currently provides an implementations are shown in Table 2. In total, Ebi currently has 30 commands. For a full overview of commands and their inputs and outputs, please refer to the manual, accessible through http://ebitools.org.

Ebi has been used in the experiments described in several recent papers published by the author team [12,15,16]. In these experiments, Ebi has shown to be me much faster than corresponding, earlier, implementations in other frameworks. This is presumably partly due to implementing these techniques a second time, though perhaps also due to the lower level access to computing

Ebi is a framework for stochastic process mining. It offers exact arithmetic computation and, currently, over 30 algorithms related to stochastic process mining, ranging from completeness estimation to analysis, conformance checking, discovery, visualisation and statistical tests. For technique implementers, Ebi handles the input and output file handling: techniques only need to define their input and output format, and Ebi will take care of transformations automatically. Currently, Ebi is a command-line based tool, however, in future work, it is intended that Ebi can serve as a high speed background library for existing process mining frameworks such as BupaR, ProM and Pm4py.