Process log recognition method based on internal state interpretation of gated recurrent neural network

Abstract

The present invention discloses a process log identification method based on the interpretation of the internal state of a gated recurrent neural network. This method belongs to the intersection of business process management and deep learning, and includes the following steps: mining a Petri net model from the process log recorded by a business information system, automatically generating a sequence set from the Petri net model, constructing its reachability graph, obtaining reachable states and constructing a reachable state set; collecting process log cases, training a classification and recognition model, and classifying hidden states to obtain hidden state classes; defining a mapping function to establish a mapping relationship between the hidden state class and the reachable state set of the Petri net reachability graph; and classifying and identifying process logs based on the gated recurrent neural network that has completed training and internal state interpretation. The present invention utilizes Petri nets to effectively improve the interpretability of the internal state of the gated RNN, enabling better process log classification and identification, as well as management of business processes and their process logs.

Description

Technical Field

[0001] The present invention belongs to the intersection of business process management and deep learning, and specifically relates to a process log identification method based on the internal state interpretation of a gated recurrent neural network. Background Art

[0002] Process mining is a key research area in business process management, aiming to uncover useful information from process logs recorded by enterprise information systems. Initial approaches to process mining focused on descriptive and diagnostic process analysis, such as discovering business processes or analyzing bottlenecks from logs. In recent years, identifying process logs and analyzing their consistency with process models, as a branch of process mining, has become an increasingly important research topic. This approach can detect deviations from desired process execution and provide timely interventions, providing a strong guarantee for enterprise success.

[0003] Numerous studies have shown that gated recurrent neural network (RNN) models can provide robust, consistent, and accurate classification and recognition for target tasks. However, due to the "black box" nature of neural networks, deep learning technologies such as RNNs lack the interpretability of their results, internal reasoning processes, and recommended execution plans. For example, it is impossible to verify the effectiveness and reliability of the model, and it is impossible to determine the rationality of the prediction model's judgment, resulting in a lack of trust in and reliance on deep learning models. More importantly, due to the lack of interpretability, neural network models are unable to effectively and accurately crop and sample their input process logs to achieve optimal classification and recognition performance when performing process log legitimacy recognition and judgment. Summary of the Invention

[0004] In order to solve the above problems, the present invention proposes a process log identification method based on the internal state interpretation of a gated recurrent neural network. By introducing Petri nets, the interpretability of the internal state of the gated recurrent neural network is improved, thereby effectively identifying process logs.

[0005] The technical solutions of the present invention are as follows:

[0006] A process log recognition method based on internal state interpretation of a gated recurrent neural network includes the following steps:

[0007] Step 1: Use a process mining algorithm to mine and reconstruct a Petri net model from the process log recorded in the business information system. The Petri net model automatically generates a sequence set. At the same time, the reachability graph is obtained according to the Petri net reachability graph construction algorithm. The reachable states are obtained based on the reachability graph to construct a reachable state set.

[0008] Step 2: Collect process log cases, train the classification recognition model, and classify the latent states to obtain the latent state classes. The specific process is as follows:

[0009] Step 2.1: Perform case statistics on the process logs recorded in the business information system to obtain the task activity sequence corresponding to each case, and generate a prefix sequence set of all task activity sequences;

[0010] Step 2.2: Use the last task activity in the prefix sequence set as the classification label, and use the prefix sequence set and the sequence set generated by the Petri net as input to train the gated recurrent neural network classification and recognition model. Use the classifier function MLP Classifier to identify the prefix sequence, decode and classify the hidden state of the gated recurrent neural network, and obtain the hidden state class of the gated recurrent neural network.

[0011] Step 2.3: Use t-SNE to reduce the dimensionality of the hidden state and visualize the hidden state of the gated recurrent neural network.

[0012] Step 3: Define a mapping function to establish a mapping relationship between the hidden state class of the gated recurrent neural network and the reachable state set of the Petri net reachable graph; thereby, the logical relationship between the hidden state classes within the gated recurrent neural network is explained through the reachable relationship of the Petri net reachable graph;

[0013] Step 4: Classify and identify the process logs based on the gated recurrent neural network that has completed training and internal state interpretation, and achieve accurate cropping and sampling of the process logs.

[0014] Furthermore, in step 1, the process mining algorithm adopted is a frequency-based inductive mining algorithm. The specific process is: first, filter out low-frequency cases in the process log to obtain a process log containing high-frequency cases; then, use the process log with high-frequency cases to find a reasonable process model; the reconstructed Petri net model includes concurrent and loop structures.

[0015] Furthermore, in step 2, the neuron implementation methods of the gated recurrent neural network include two methods: long short-term memory artificial neural network LSTM and gated recurrent unit GRU; according to the process log of the business information system, the task activity sequence corresponding to each case is obtained, and a prefix sequence set of all task activity sequences is generated; the sequence set is automatically generated according to the Petri net model; the prefix set of the task activity sequence and the sequence set generated by the Petri net are input into the LSTM-RNN or GRU-RNN of the gated recurrent neural network for training, and the MLP classifier function MLP Classifier is used to realize decoding and classification of the hidden state of the gated recurrent neural network. When the model is iteratively trained, the input at this moment and the output at the previous moment are included.

[0016] Furthermore, in step 3, a mapping relationship u:V→Ω is defined, where V represents the set of hidden state classes of the gated recurrent neural network, Ω represents the transcendental set of the reachable state set of the reachable graph of the Petri net, and each element of the transcendental set is a reachable state set; the notation is introduced t i Represents the triggering task activity of the reachable state set, i is the sequence number of the task activity; If and only if Among them, v represents the hidden state class and M represents the reachable state set.

[0017] Furthermore, the logic of the transcendental set algorithm for obtaining the reachable state set from the Petri net reachable graph is as follows: first, traverse each task activity and its corresponding reachable state in the Petri net reachable graph; then, put the task activity t i The set of possible reachable states after initiation is recorded as {t i |-M i}; If the task is active t i The number of possible reachable states after triggering is greater than or equal to two, and the task activity t i The different possible reachable state sets after triggering are recorded as {t i |-M i ,M′ i ,……}; In addition, if the possible reachable states after different task activities are the same, the set of possible reachable states after different task activities is recorded as {t i ,t j ,……|-M i}, t i , t i Represents different task activities, i and j are the serial numbers of task activities; finally, put these sets into a transcendental set to obtain the transcendental set Ω of the reachable state set of the Petri net reachable graph; where M i and M′ i Represents task activity t i Different reachable states after triggering.

[0018] The beneficial technical effects brought about by the present invention are:

[0019] The present invention proposes a new method for the internal state interpretation device of a gated recurrent neural network for process log identification. It not only uses Petri nets to effectively improve the interpretability of the internal state of gated (including LSTM and GRU) recurrent neural networks, but also can better train the gated recurrent neural network on this basis, improve the process log classification and identification capabilities, so as to better manage business processes and their process logs to meet the growing business needs. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is a framework diagram of the process log identification method based on the internal state interpretation of the gated recurrent neural network of the present invention;

[0021] Figure 2 It is a diagram of the generation process of the Petri net reachability graph in the present invention;

[0022] Figure 3 This is a framework diagram for training the gated recurrent neural network classification and recognition model in the present invention;

[0023] Figure 4 It is an abstract representation of the hidden state classification of the gated recurrent neural network in the present invention;

[0024] Figure 5 It is a mapping relationship diagram from the hidden state class of the gated recurrent neural network to the reachable state set of the Petri net reachable graph in the present invention, and a gated recurrent neural network hidden state interpretation diagram based on the Petri net reachable graph. DETAILED DESCRIPTION

[0025] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0026] One approach to making gated recurrent neural networks (GRNs) interpretable is to use visible tasks to explain GRNs on unseen tasks. In specific scenarios, GRN models are simulated using visible tasks to verify that the GRNs produce consistent results each time they are run.

[0027] In terms of process log recognition, structured process models belong to visible tasks, which can explain deep learning models and simulate the internal operation of gated recurrent neural networks. Furthermore, Petri nets are a modeling language for business processes and can effectively handle special structures such as concurrency and loops in business processes. The reachability graph of Petri nets is composed of reachable states and reachable relationships, which clearly depicts the state changes after the transition is triggered. This is extremely similar to the internal operation of gated recurrent neural networks. For this reason, the use of structured Petri nets and their reachability graphs can well explain the internal operating mechanism of gated recurrent neural networks. Therefore, the present invention introduces Petri nets to interpret the internal states of gated recurrent neural networks and applies them to process log recognition.

[0028] Figure 1It is a framework diagram for the implementation of the present invention, including mining Petri nets from process logs recorded by a business information system according to a process mining algorithm, obtaining its reachable graph according to a Petri net reachable graph construction algorithm, obtaining the task activity sequence corresponding to each case according to the process logs recorded by the business information system and generating a prefix sequence set of all task activity sequences, training a gated recurrent neural network model through the prefix sequence set of the task activity sequence and the sequence set generated by the reconstructed Petri net, classifying the hidden states of the recurrent neural network using a classifier function MLP Classifier, establishing a mapping relationship between the gated recurrent neural network hidden state class and the reachable state set of the Petri net reachable graph, etc.

[0029] The specific steps of the process log recognition method based on the internal state interpretation of the gated recurrent neural network are as follows:

[0030] Step 1: Use a process mining algorithm to mine and reconstruct a Petri net model from the process log recorded in the business information system. The Petri net model automatically generates a sequence set as one of the data sequences for training the gated recurrent neural network. At the same time, the reachability graph is obtained according to the Petri net reachability graph construction algorithm, and the reachable states are obtained according to the reachability graph to construct a reachable state set. The process mining algorithm adopted by the present invention is an inductive mining algorithm based on frequency (Inductive Miner-infrequent, IMi). The specific process is as follows: first, filter out cases with lower frequency in the process log, that is, non-frequent behaviors, and obtain a process log containing cases with higher frequency. Then, use the process log with cases with higher frequency to find a reasonable process model. In addition, IMi is implemented in the InductiveMiner package of the ProM framework. The reachability graph construction algorithm is implemented using the ProM framework plug-in Construct Reachability Graph of a Petri Net.

[0031] Figure 2This is an embodiment of the reachable graph of the Petri net of the present invention. First, based on the process log recorded by the business system, the Petri net is reconstructed through the process mining algorithm. The reconstructed Petri net model can handle parallel structures, including special structures such as concurrency and loops. This can better explain the sequence recognition problem of the process log of the gated recurrent neural network. For example, in this embodiment, the Petri net model is reconstructed based on the actual hospital bill process log. The model includes task activity A, task activity M, task activity H, task activity N, task activity B, task activity C, task activity K, task activity D, task activity Q, task activity E, and task activity I; wherein, task activities B and C form a concurrent structure, and task activities E and I form a loop structure. The black task activities in the Petri net model are invisible task activities and have no practical meaning. Then, through the Petri net reachable graph construction algorithm, it can be obtained Figure 2 The reachable graph of the Petri net shown in the figure further forms the reachable state set {M0,M1,M2,M3,M4,M5,M6,M7,M8,M9,M end}, and then used to query the mapping relationship between its gated recurrent neural network hidden state class and the reachable state set of the reachable graph. The present invention does not consider the reachable states in the reachable graph that do not trigger task activities. In addition, the hospital billing process log of the present invention is obtained and integrated from the financial module of the ERP system of a regional hospital. It contains events related to the billing of medical services provided by the hospital. Each trace records the coarse-grained task activities performed for the billing of a bundled package of medical services, and does not contain information about the actual medical services provided by the hospital. The link to the actual process log is https: / / data.4tu.nl / articles / dataset / Hospital_Billing_-_Event_Log / 12705113. Task activity A represents new method (NEW), task activity M represents change end (CHANGE END), task activity H represents change diagnosis (CHANGE DIAGN), task activity N represents manual operation (MANUAL), task activity B represents FIN (FIN), task activity C represents release (RELEASE), task activity K represents code not determined (CODE NOK), task activity D represents code determined (CODE OK), task activity Q represents ZDBC_BEHAN (ZDBC_BEHAN), task activity E represents billing (BILLED), and task activity I represents not stored (STORNO).

[0032] Step 2: Collect process log cases, train the classification recognition model, and classify the latent states to obtain the latent state classes. The specific process is as follows:

[0033] Step 2.1: Perform case statistics on the process logs recorded in the business information system to obtain the task activity sequence corresponding to each case, and generate a prefix sequence set of all task activity sequences;

[0034] Step 2.2: Use the last task activity in the prefix sequence set as the classification label, and use the prefix sequence set and the sequence set generated by the Petri net as input to train the gated recurrent neural network classification and recognition model. Use the classifier function MLP Classifier to identify the prefix sequence, decode and classify the hidden state of the gated recurrent neural network, and obtain the hidden state class of the gated recurrent neural network.

[0035] The gated recurrent neural network classification and recognition model training framework of the present invention is as follows Figure 3 As shown, there are two ways to implement neurons in the gated recurrent neural network: long short-term memory artificial neural network (abbreviated as: LSTM) and gated recurrent unit (abbreviated as: GRU). According to the process log of the business information system, the task activity sequence corresponding to each case is obtained, and the prefix sequence set of all task activity sequences is generated; the sequence set is automatically generated according to the Petri net model. The prefix sequence set of the task activity sequence and the sequence set generated by the Petri net are input into the LSTM-RNN or GRU-RNN of the gated recurrent neural network for training, and the MLP classifier function MLP Classifier is used to realize decoding and classification of the hidden state of the gated recurrent neural network. When the model is iteratively trained, the input at this moment and the output at the previous moment are included. Among them, x0, x1,…, x n Represent the input of the gated recurrent neural network at different times, y0, y1, ..., y n They represent the outputs of the gated recurrent neural network at different times, and (0,1,…,n) represents different times.

[0036] The present invention inputs prefix sequences, trains a gated recurrent neural network model, and analyzes its hidden states. It reveals that the relationships between hidden states exhibit certain regularities. This is reflected in the fact that the changes in different hidden states are similar to their corresponding Petri net reachability graphs. By simulating the running trajectories of different prefix sequences based on the reachability graphs, the interpretability of the hidden states within the gated recurrent neural network is improved.

[0037] Step 2.3: Use the t-SNE (t-distributed stochastic neighbor embedding) method to reduce the dimensionality of the hidden state and visualize the hidden state of the gated recurrent neural network.

[0038] Figure 4 It is an abstract representation of the hidden state class of the gated recurrent neural network of this invention, and the dimension of the hidden state is reduced and visualized through t-SNE. Figure 4In the gated recurrent neural network, the hidden state set V = {v A ,v M ,v H ,v N ,v B ,v C ,v K ,v D ,v Q ,v E ,v I} contains several elements, element v A Represents the hidden state class corresponding to task activity A, element v M Represents the hidden state class corresponding to the task activity M, element v H Represents the hidden state class corresponding to the task activity H, element v N Represents the hidden state class corresponding to the task activity N, element v B Represents the hidden state class corresponding to task activity B, element v C Represents the hidden state class corresponding to the task activity C, element v K Represents the hidden state class corresponding to the task activity K, element v D Represents the hidden state class corresponding to the task activity D, element v Q Represents the hidden state class corresponding to the task activity Q, element v E Represents the hidden state class corresponding to the task activity E, element v I Represents the hidden state class corresponding to task activity I.

[0039] Step 3: Define a mapping function to establish a mapping relationship between the hidden state class of the gated recurrent neural network and the set of reachable states in the Petri net reachability graph. Thus, the logical relationship between the hidden state classes within the gated recurrent neural network can be explained through the reachability relationship of the Petri net reachability graph.

[0040] Figure 5 This is an embodiment of the mapping relationship between the hidden state class of the gated recurrent neural network and the reachable state set of the Petri net reachable graph of the present invention, as well as a schematic diagram of the gated recurrent neural network hidden state explained based on the Petri net reachable state set. The present invention defines the mapping relationship u:V→Ω, which is the mapping relationship from the hidden state class of the gated recurrent neural network to the reachable state set of the Petri net reachable graph. In other words, the notation is introduced t i Represents the triggering task activity of the reachable state set (ie, the transition of the reachable graph, for example, in the embodiment of the present invention, t i ∈{A,M,H,N,B,C,K,D,Q,E,I}), i is the sequence number of the task activity. If and only if Where V represents the set of hidden state classes of the gated recurrent neural network, Ω represents the transcendental set of the reachable state set of the reachable graph of the Petri net, and each element of the transcendental set refers to the reachable state set.

[0041] In the embodiment of the present invention, the transcendental set Ω of the reachable state set of the reachable graph of the Petri net is = {{A|-M1},{M,H|-M2},{N|-M3},{B|-M4,M6},{C|-M5,-M6},{K|-M7},{D|-M8},{Q,I|-M9},{E|-M end}}. Among them, for each element of the transcendental set Ω, {A|-M1} represents the set of possible reachable states after task activity A triggers. {M,H|-M2} represents the set of possible reachable states after task activities M and H with conflicting relationships triggers. {N|-M3} represents the set of possible reachable states after task activity N triggers. From the reachability graph, it can be seen that there is a concurrent relationship between task activities M and H. Among them, {B|-M4,M6} represents the set of possible reachable states after task activity B triggers. {C|-M5,M6} represents the set of possible reachable states after task activity C triggers. {K|-M7} represents the set of possible reachable states after task activity K triggers. {D|-M8} represents the set of possible reachable states after task activity D triggers. {Q,I|-M9} represents the set of possible reachable states after task activities Q and I triggers. Furthermore, I records possible cyclic behaviors. {E|-M end} refers to the set of possible reachable states after task activity E is triggered.

[0042] The transcendental set algorithm for obtaining the reachable state set from the Petri net reachable graph is shown in Algorithm 1. First, traverse each task activity and its corresponding reachable state in the Petri net reachable graph. Then, the task activity t i The set of possible reachable states after initiation is recorded as {t i |-M i If the task is active t i The number of possible reachable states after triggering is greater than or equal to two, and the task activity t i The set of possible reachable states after initiation is recorded as {t i |-M i ,M′ i ,……}. In addition, if different task activities t i With t j (i, j are the serial numbers of task activities) and the possible reachable states after triggering are the same, then the task activity t i With t j The set of possible reachable states after the triggering is recorded as {t i ,tj ,……|-M i Finally, these sets are put into a transcendental set to obtain the transcendental set Ω of the reachable state set of the Petri net reachable graph.

[0043]

[0044] Using the mapping relationship u:V→Ω, the mapping relationship from the hidden state class of the gated recurrent neural network to the reachable state set of the Petri net reachable graph is obtained.

[0045] Specifically, in the embodiment of the present invention, the hidden state class v corresponding to the task activity A is A Mapped to the set of possible reachable states {M1} after task activity A is triggered. The hidden state class v corresponding to task activity M M Mapped to the set of possible reachable states {M2} after the task activity M is triggered, the hidden state class v corresponding to the task activity H H The set of possible reachable states after the task activity H is mapped is also {M2}. The hidden state class v corresponding to the task activity N N Mapped to the set of possible reachable states {M3} after task activity N is triggered. The hidden state class v corresponding to task activity B B Mapped to the set of possible reachable states {M4,M6} after task activity B is triggered. The hidden state class v corresponding to task activity C C Mapped to the set of possible reachable states {M5,M6} after the task activity C is triggered. The hidden state class v corresponding to the task activity K K Mapped to the set of possible reachable states {M7} after the task activity K is triggered. The hidden state class v corresponding to the task activity D D Mapped to the set of possible reachable states {M8} after the task activity D is triggered. The hidden state class v corresponding to the task activity Q Q Mapped to the set of possible reachable states {M9} after the task activity Q is triggered, the hidden state class v corresponding to the task activity I I The set of possible reachable states mapped to task activity I is also {M9}. The hidden state class corresponding to task activity E is mapped to the set of possible reachable states after task activity E is triggered {M end}.

[0046] Regarding the explanation of the hidden state class of gated recurrent neural networks based on Petri net reachability graph, first, given a single prefix sequence<A,M,N,B,C,K> , its execution trajectory on the reachable graph and the corresponding hidden state class is represented by the dotted arrows Then, for a single prefix sequence<A,H,N,B,C,K> , its execution trajectory is shown using the dotted arrows Similarly, for other prefix sequences, by simulating their running trajectories, we can see that the relationship between the hidden states shows a certain regularity. The changes between different hidden states are similar to their corresponding reachable graphs, as shown in the following example: Figure 5 As shown in the figure, A, M, H, N, B, C, and K represent the task activities of the prefix sequence, i.e., the transitions of the reachable graph. For convenience, the transitions of the present invention are collectively referred to as task activities.

[0047] Step 4: Classify and identify the process logs based on the gated recurrent neural network that has completed training and internal state interpretation, and achieve accurate cropping and sampling of the process logs.

[0048] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the scope of protection of the present invention.

Claims

1. A process log recognition method based on internal state interpretation of gated recurrent neural networks, characterized in that: The steps include: Step 1: Use a process mining algorithm to mine and reconstruct a Petri net model from the process log recorded in the business information system. The Petri net model automatically generates a sequence set. At the same time, the reachability graph is obtained according to the Petri net reachability graph construction algorithm. The reachable states are obtained based on the reachability graph to construct a reachable state set. Step 2: Collect process log cases, train the classification recognition model, and classify the latent states to obtain the latent state classes. The specific process is as follows: Step 2.1: Perform case statistics on the process logs recorded in the business information system to obtain the task activity sequence corresponding to each case, and generate a prefix sequence set of all task activity sequences; Step 2.2: Use the last task activity in the prefix sequence set as the classification label, and use the prefix sequence set and the sequence set generated by the Petri net as input to train the gated recurrent neural network classification and recognition model. Use the classifier function MLP Classifier to identify the prefix sequence, decode and classify the hidden state of the gated recurrent neural network, and obtain the hidden state class of the gated recurrent neural network. Step 2.3: Use t-SNE to reduce the dimensionality of the hidden state and visualize the hidden state of the gated recurrent neural network. Step 3: Define a mapping function to establish a mapping relationship between the hidden state class of the gated recurrent neural network and the reachable state set of the Petri net reachable graph; thereby, the logical relationship between the hidden state classes within the gated recurrent neural network is explained through the reachable relationship of the Petri net reachable graph; Step 4: Classify and identify the process logs based on the gated recurrent neural network that has completed training and internal state interpretation, and achieve accurate cropping and sampling of the process logs.

2. The process log identification method based on the internal state interpretation of the gated recurrent neural network according to claim 1 is characterized in that: In step 1, the process mining algorithm used is a frequency-based inductive mining algorithm. The specific process is as follows: first, low-frequency cases in the process log are filtered out to obtain process logs containing high-frequency cases; then, the process logs containing high-frequency cases are used to discover a reasonable process model; The reconstructed Petri net model includes concurrent and cyclic structures.

3. The process log identification method based on the internal state interpretation of the gated recurrent neural network according to claim 1 is characterized in that: In step 2, there are two ways to implement neurons in the gated recurrent neural network: a long short-term memory artificial neural network (LSTM) and a gated recurrent unit (GRU); based on the process log of the business information system, the task activity sequence corresponding to each case is obtained, and a prefix sequence set of all task activity sequences is generated; a sequence set is automatically generated based on a Petri net model; the prefix set of the task activity sequence and the sequence set generated by the Petri net are input together into the LSTM-RNN or GRU-RNN of the gated recurrent neural network for training, and the MLP classifier function MLP Classifier is used to decode and classify the hidden state of the gated recurrent neural network. When the model is iteratively trained, the input at this moment and the output at the previous moment are included.

4. The process log identification method based on the internal state interpretation of the gated recurrent neural network according to claim 1 is characterized in that: In step 3, a mapping relationship u:V→Ω is defined, where V represents the set of hidden state classes of the gated recurrent neural network, Ω represents the transcendental set of the reachable state set of the reachable graph of the Petri net, and each element of the transcendental set is a reachable state set; the notation is introduced t i Represents the triggering task activity of the reachable state set, i is the sequence number of the task activity; If and only if Among them, v represents the hidden state class and M represents the reachable state set.

5. The process log identification method based on the internal state interpretation of the gated recurrent neural network according to claim 4 is characterized in that: The logic of the transcendental set algorithm for obtaining the reachable state set from the Petri net reachable graph is as follows: first, traverse each task activity and its corresponding reachable state in the Petri net reachable graph; then, put the task activity t i The set of possible reachable states after initiation is recorded as {t i |-M i }; If the task is active t i The number of possible reachable states after triggering is greater than or equal to two, and the task activity t i The different possible reachable state sets after triggering are recorded as {t i |-M i ,M′ i ,……}; In addition, if the possible reachable states after different task activities are the same, the set of possible reachable states after different task activities is recorded as {t i ,t j ,……|-M i }, t i , t i Represents different task activities, i and j are the serial numbers of task activities; finally, put these sets into a transcendental set to obtain the transcendental set Ω of the reachable state set of the Petri net reachable graph; where M i and M′ i Represents task activity t i Different reachable states after triggering.

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