Software testing is an important problem to design a large software system and it is difficult to be solved due to its computational complexity. We try to use program nets to approach this problem. As the first step towards solving software testing problem, this paper provides a technique to generate subnets of a program net and applies this technique to software testing. Firstly, definitions and properties of program nets are introduced based on our previous works, and the explanation of software testing problem is given. Secondly, polynomial algorithms are proposed to generate subnets that can cover all the given program net. Finally, a case study is presented to show how to find subnets covering a given program net by using the proposed algorithms, as well as to show the input test data of the program net for software testing.

This paper proposes methods of computing maximum throughput for Petri nets that model workflows including resources, called WF-nets with resources. We first propose the formal definitions of WF-nets with resources and their subclasses: marked graph/state machine WF-nets with conflict-free resources (CF-Res-MG/SMWF-nets). We also show several properties of CF-Res-MG/SMWF-nets. Next we give the methods of computing maximum throughput for CF-Res-MG/SMWF-nets under condition that all tokens have to be processed in the order of First-In First-Out (FIFO). Concretely, for CF-Res-MGWF-nets, on the basis of Ramamoorthy's method of computing cycle time, we give an algorithm of computing maximum throughput under the FIFO condition. For CF-Res-SMWF-nets, there is not any method of computing maximum throughput under the FIFO condition. So we are the first to give an algorithm of computing maximum throughput for CF-Res-SMWF-nets under the FIFO condition. Finally we show an example of computing maximum throughput by using our method.

This paper provides a list-scheduling method for program nets executed with two processors. The program nets dealt with in this paper are acyclic and SWITCH-less, and the priority list proposed in this paper consists of both dynamic and static lists. First, we point out the weakness of a previously proposed priority list and propose a new priority list. Then we give properties of the new priority list and further prove this new priority list can generate optimal schedules for the program nets whose AND-nodes possess at most single input edge. Finally, we compare the new priority list with the previous one to show the new priority list can generate shorter schedules than the previous for the nets whose AND-nodes may have two input edges.

In our privious paper, we proposed an algorithm that determines delay times of a timed Petri net from the structural information of a signaling pathway, but Petri net structures containing cycles and inhibitory arcs were not considered. This paper provides conditions for cycle-contained Petri nets to have reasonable delay times. Furthermore, handling of inhibitory arcs are discussed in terms of the reaction rate of inhibitory interaction in signaling pathway, especially the conversion process of Petri net with inhibitory arc to the one without inhibitory arc is given.

Topological sorting is, given with a directed acyclic graph G=(V,E), to find a total ordering of the vertices such that if (u,v)E then u is ordered before v. Instead of topological sorting, we are interested in how many total orderings exist in a given directed acyclic graph. We call such a total ordering as legal sequence and the problem of finding total number of legal sequences as legal sequence number problem. In this paper, we firstly give necessary definitions and known results obtained in our previous research. Then we give a method how to obtain legal sequence number for a class of directed acyclic graphs, extended 2-b-SPGs. Finally we discuss the complexity of legal sequence number problem for extended 2-b-SPGs.

A workflow is a flow of work carried out by workers, and workflow management is to automate the flow of work. In workflow management, an actual work is carried out based on the workflow, which is called case. In order to effectively meet various requirements, it is necessary to change current workflow dynamically, which is called dynamic workflow change. When the dynamic change is required, there exist cases in the workflow. In order to handle these cases and further to keep the queuing order, the dynamic change takes period of time (called transient time) until the changed workflow becomes steady state again. During the transient time, workers are forced to do irregular work, and therefore it is important to clarify if a change type takes shorter transient time. In this paper, we do the performance evaluation on transient time of dynamic workflow changes. To do so, we first give a definition of transient time, and then propose methods of computing transient time of three change types proposed by Ellis et al. Finally, we do the performance evaluation for 90 dynamic changes by computing the transient times.

This paper deals with the performance evaluation of two types of dynamic change, called Flush and SCO (Synthetic Cut-Over), for state machine WF-nets. As an evaluation measure of dynamic change for marked graph WF-nets, change time has been used. We first generalize change time so as to apply it to dynamic change for state machine WF-nets. By using its maximum value, we evaluate the worst-case of dynamic change for state machine WF-nets. We call the maximum value as worst change time. Then under the same assumptions as our previous studies, we give methods of calculating worst change time of Flush and SCO dynamic changes. We also clarify the relation on worst change time between them. Finally we evaluate them by comparing the values of worst change time for an actual example of dynamic change.

PARAdeg has been defined to try to measure parallelism inherent in a program net. Studies on computation of PARAdeg have been done, but the quantitative evaluation, on how much PARAdeg fits parallelism of program nets, has not been studied. In this paper, we do the evaluation by applying genetic algorithm to measure firing completion times when PARAdeg processors, and less and more processors are provided for 400 program nets. Our experimental results show that the firing completion times decrease rapidly with increase of processors till PARAdeg and slowly when processors are increased to more than PARAdeg, which implies PARAdeg is a reasonable standard to measure parallelism of program nets.

In this paper, we discuss the parallel degree of well-structured workflow nets, WF-nets, for short. First, we give the definition of parallel degree, PARAdeg, for WF-nets. Second, we show it is intractable to compute the value of PARAdeg for acyclic well-structured WF-nets. Next we construct two heuristic algorithms to compute the value. The first algorithm is focused on nest structure and the second one is focused on the longest path. Finally, we perform an experiment to compare the two algorithms and the result is that the accuracy of the first algorithm based on nest structure was higher than that of the second one based on the longest path for most well-structured WF-nets and the accuracy of the second one is better than that of first one only when the well-structured workflow nets are mainly composed by the parallel structures.

This paper deals with two-processor nonpreemptive scheduling problem for acyclic SWITCH-less program nets including two types of nodes: AND-node and OR-node. Compared with task graphs that are a special case of acyclic SWITCH-less program nets and include only AND-nodes, the multiprocessor scheduling problem of general acyclic SWITCH-less program nets is more complicated. Since multiprocessor scheduling problem for general task graphs is NP-hard, so is for acyclic SWITCH-less program nets generally. In this paper, we suppose the acyclic SWITCH-less program nets satisfy: (i) each AND-node and OR-node have 1 and 0 node firing time, respectively; (ii) each AND-node possesses single input edge. For such a class of acyclic SWITCH-less program nets, we first propose a hybrid priority list L that consists of both dynamic and static sub-lists. Then we prove that, for a given acyclic SWITCH-less program net to be executed by two identical processors, the schedule generated by L is optimal.

This paper deals with WF-net based modeling and verification of interorganizational workflows (interworkflows for short) based on the protocol of WfMC. In the protocol, there are three patterns of interoperability: Chained, Nested, and Parallel synchronized; and an interworkflow is constructed by using those interoperability patterns. We first give a WF-net based modeling method. In this modeling method, the three interoperability patterns are respectively expressed in terms of WF-nets. They enable us to model a given interworkflow as a WF-net by connecting WF-nets representing its constituent workflows. We also indicate that if free choice WF-nets are connected by means of any combination of the three patterns then the resultant WF-net is asymmetric choice. Next we discuss verification of WF-nets obtained through the modeling method. Intuitively, a WF-net is said to be sound if, for any case, the initial state is always transformed to the final state. Unfortunately, even if every constituent WF-net is sound FC, the resultant WF-net is not always sound. We give a sufficient condition of non-soundness checkable in polynomial time. We also show that if they are connected by only the Nested pattern then the resultant WF-net is sound.

Topological sorting is, given with a directed acyclic graph G = (V, E), to find a total ordering of the vertices such that if (u, v) E then u is ordered before v. Instead of finding total orderings, we wish to find out how many total orderings exist in a given directed acyclic graph G = (V, E). Here we call a total ordering as legal sequence and the problem as legal sequence number problem. In this paper, we first propose theorems on equivalent transformation of graphs with respect to legal sequence number. Then we give a formula to calculate legal sequence number of basic series-parallel digraphs and a way of the calculation for general series-parallel digraphs. Finally we apply our results to show how to obtain legal sequence number for a class of extended series-parallel digraphs.

This paper proposes a public-key cryptography by applying RSA and Petri nets. We introduce RSA and a Petri net based private-key cryptography and then taking the advantages of these two cryptography, we propose a new public-key cryptography, PNPKC. To compare with RSA on security as well as computation order, we do simulation experiments. As the results, the security of PNPKC is as strong as RSA cryptography, and the encryption and decryption of PNPKC are in average 239 times as fast as RSA cryptography from our experiments. Besides, to see if our current PNPKC program can be practically used, we do comparative experiment with PGP, which shows PNPKC takes computation time in average as much as 36 times of PGP cryptography. That means our PNPKC program still needs to be technically improved.

This paper aims at improving effectiveness of previously proposed hybrid priority lists, {L*i=LdLsi}, that are applied in nonpreemptive 2-processor scheduling of general acyclic SWITCH-less program nets, where Ld and Lsi are dynamic and static priority lists respectively. Firstly, we investigate the effectiveness of Ld through experiments. According to the experimental results, we reconstruct Ld to propose its improved list L1d. Then analyzing the construction methodology of the static priority lists {Lsi}, we propose a substituted list L2d by taking into account of the factor: remaining firing numbers of nodes. Finally, we combine a part of L1d and L2d to propose a new priority list L**. Through scheduling simulation on 400 program nets, we find the new priority list L** can generate shorter schedules, close to ones of GA (Genetic Algorithm) scheduling that has been shown exceedingly effective but costing much computation time.

This paper investigates the usefulness of a new priority list for two-processor scheduling problem of program nets. Firstly, we discuss the weakness of a previously proposed priority list and then introduce a new priority list. Through simulation experiment we show that the new priority list is better than the previous one and can generate the same length of schedules as GA scheduling, which implies the new priority list can generate approximately optimal schedules.

This paper proposes a new change type for dynamic change of workflows, named Selective Shift. Workflow technology is being introduced in many companies. Workflows are business processes that allow for computerized support. The goal of workflow technology is to process workflow instances, called cases, as efficiently as possible. Companies need to change their workflows in order to adapt them to various requirements. Dynamic change is to change workflows having running cases. The most important issue in dynamic change is how running cases should be handled. Ellis et al. and Sadiq et al. have proposed change types that prescribe how to handle running cases. Their change types handle running cases collectively. If a change type can handle running cases separately, the change type would be more flexible and efficient than the conventional change types. However, there is no any change type that can handle running cases separately. Selective Shift to be proposed can handle running cases separately. We first present the concept and definition of Selective Shift. Then we give a method to handle running cases separately. Furthermore we give methods to handle running cases so that dynamic change becomes most efficient on one evaluation measure, called change time. Finally we compare Selective Shift with the conventional change types on change time by using 270 examples of dynamic change.

Automatic detection of prohibited items is vital in helping security staff be more efficient while improving the public safety index. However, prohibited item detection within X-ray security inspection images is limited by various factors, including the imbalance distribution of categories, diversity of prohibited item scales, and overlap between items. In this paper, we propose to leverage the Poisson blending algorithm with the Canny edge operator to alleviate the imbalance distribution of categories maximally in the X-ray images dataset. Based on this, we improve the cascade network to deal with the other two difficulties. To address the prohibited scale diversity problem, we propose the Re-BiFPN feature fusion method, which includes a coordinate attention atrous spatial pyramid pooling (CA-ASPP) module and a recursive connection. The CA-ASPP module can implicitly extract direction-aware and position-aware information from the feature map. The recursive connection feeds the CA-ASPP module processed multi-scale feature map to the bottom-up backbone layer for further multi-scale feature extraction. In addition, a Rep-CIoU loss function is designed to address the overlapping problem in X-ray images. Extensive experimental results demonstrate that our method can successfully identify ten types of prohibited items, such as Knives, Scissors, Pressure, etc. and achieves 83.4% of mAP, which is 3.8% superior to the original cascade network. Moreover, our method outperforms other mainstream methods by a significant margin.

The notion of speedup has been extensibly used in performance analysis of parallel program executions by multi-processor systems. In this paper, based on this notion, a definition of parallel degree is proposed to theoretically evaluate the parallelism of data-flow program nets, and its computation method is given. Further the fitness of the definition for the parallelism is discussed, and finally an application is suggested to estimate the number of processors required to run a given program net with a reasonable speedup.