## 5 Process Analyzing Functionality
### The Structural Analysis of Rediscovered XPDL Process Models
then
33:\(w\gets u\); \(\Omega.A^{bs}\leftarrow\Omega.A^{bs}\cup\{w\}\);
34:\(\Omega.\varrho_{o}(\
u)\gets w\); \(\Omega.\varrho_{i}(w)\gets v\); \(\Omega.\beta_{o}(\
u)\leftarrow\kappa_{o}(s)\); \(\Omega.\beta_{i}(\
u)\leftarrow\kappa_{i}(s)\);
35:\(\phi_{o}((w,o\in\varrho_{o}(w)))\leftarrow\) occurrences of \(o\in\varrho_{o}(w)\);
36:\(\phi_{i}((e\in\varrho_{i}(w),w))\leftarrow\) occurrences of \(Definition 2: Behavioral sequence net of a rediscovered SICN (or XPDL) process model model. Let \(\Omega\) be a **BSN**, a behavioral sequence net that is formally defined as \(\Omega=(\varrho,\kappa,o)\) over the discovered workitems, \(\mathbf{A}^{bs}\), and the discovered control-transitions, \(\mathbf{T}^{bs}\), where  
* \(\varrho=\varrho_{i}\cup\varrho_{o}\) where, \(\varrho_{o}:\mathbf{A}^{bs}\longrightarrow\wp(\mathbf{A}^{bs})\) is a multivalued mapping of a workitem to its immediate successor, and \(\varrho_{i}:\mathbf{A}^{bs}\longrightarrow\wp(\mathbf{A}^{bs})\) is a multivalued mapping of a workitem to its immediate predecessor;
* \(\beta=\beta_{i}\cup\beta_{o}\) where, \(\beta_{i}\): \(\mathbf{A}^{bs}\longrightarrow\mathbf{T}^{bs}\) is a single-valued mapping of a workitem to its connected control-transition, \(\tau\), \((\
u\in\varrho_{i}(\alpha),\alpha)\in\mathbf{T}^{bs}\); and \(\beta_{o}\): \(\mathbf{A}^{bs}\longrightarrow\mathbf{T}^{bs}\) is a single-valued mapping of a workitem to its connected control-transition, \(\tau\), \((\alpha,\
u\in\varrho_{o}(\alpha))\in\mathbf{T}^{bs}\), where \(\alpha\in\mathbf{A}^{bs}\);
* \(o=o_{i}\cup o_{o}\) where, \(o_{i}\): \(\mathbf{T}^{bs}\longrightarrow\mathbf{N}\) is a single-valued mapping of an incoming control-transition (\(\tau\in\beta_{i}\)) to its number of occurrences; and \(o_{o}\): \(\mathbf{T}^{bs}\longrightarrow\mathbf{N}\) is a single-valued mapping of an outgoing control-transition (\(\tau\in\beta_{o}\)) to its number of occurrences. The behavioral analysis functionality illustrated in Figure 6 and devised in Algorithm 2 is able to produce a set of behavioral sequence nets from the rediscovered SICN/XPDL process model. Our emphasis is placed on the quality analysis of rediscovered process model by using the proposed concept and its algorithm. That is, the behavioral analysis aims at improving the quality of the rediscovered process model. Thus, naturally the following questions are raised: what is the quality of a process model? How can we evaluate the quality of a process model? This paper tries to answer those questions through the concept of behavioral sequence nets supported by the functional integration of the process mining and the process analyzing functionalities. We would insist that the quality of a rediscovered process model be defined by the degree of the discrepancy between the discovered process model as it is built by the Buildtime subsystem and the rediscovered process model as it is rediscovered by the Miningtime subsystem. The discrepancy, as you can easily imagine, is caused by disjunctive and conjunctive process patterns presented on the corresponding process model. The number of disjunctive process patterns on the model will affect the number of _mutually exclusive behavioral sequences_, whereas the number of the conjunctive process patterns on the model will affect the number of _mutually inclusive behavioral sequences_. Additionally, the statistical measurements related to the behavioral sequences play very valuable role in evaluating the quality of the rediscovered process models. Figure 6: The behavioral analysis and statistics of the rediscovered process model. Each of the behavioral sequences can be traced through the interactive and visual operations provided by the process analyzer. Figure 7 depicts a situational snapshot of performing the interactive and visual analyses through the behavioral sequence tracer. The graph model of the behavioral sequence net was rediscovered from the dataset of the large bank transaction process enactment event logs.