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.

This paper proposes a method to incorporate the concept of time for the inclusion of dynamics of signaling pathway in a Petri net model, i.e., to use timed Petri nets. Incorporation of delay times into a Petri net model makes it possible to conduct quantitative evaluation on a target signaling pathway. However, experimental data describing detailed reactions are not available in most cases. An algorithm given in this paper determines delay times of a timed Petri net only from the structural information of it. The suitability of this algorithm has been confirmed by the results of an application to the IL-1 signaling pathway.

An automorphism of a graph G=(V, E) is such a one-to-one correspondence from vertex set V to itself that all the adjacencies of the vertices are maintained. Given a subset S of V whose one-to-one correspondence is decided, if the vertices of V-S possess unique correspondence in all the automorphisms that satisfy the decided correspondence for S, S is called determiner set of G. Further, S is called minimal determiner set if no proper subset of S is a determiner set and called kernel set if determiner set S with the smallest number of elements. Moreover, a problem to judge whether or not S is a determiner set is called determiner set decision problem. The purpose of this research is to deal with determiner set decision problem. In this paper, we firstly give the definitions and properties related to determiner sets and then propose an algorithm JDS that judges whether a given S is a determiner set of G in polynomial computation time. Finally, we evaluate the proposed algorithm JDS by applying it to possibly find minimal determiner sets for 100 randomly generated graphs. As the result, all the obtained determiner sets are minimal, which implies JDS is a reasonably effective algorithm for the judgement of determiner sets.

A data-flow program net is a graph representation of data-flow programs consisting of three types of nodes, AND-node, OR-node and SWITCH-node, which represent arithmetic/logical, data merge and context switch operations respectively. Minimum firing (completion) time T of a program net is an important element in computing parallel degree PARAdeg residing in a data-flow program and is defined as the minimum time when the program net is executed by enough many processors. In this paper, we propose algorithms to efficiently compute T by contracting AND-nodes generally for self-cleaning SWITCH-less program nets with arbitrary node firing time and give the experimental results of the algorithms to show the efficiency.

A workflow is a flow of work carried out in parallel and in series by people. In order to improve efficiency, it is required to change the current workflow dynamically. Since dynamic change of workflows may probably make the series of work inconsistent, it is necessary to find out consistent change of workflow. As consistent ways, three types of dynamic changes: flush, abort, and synthetic cut-over (SCO), have been proposed. However, the concrete analysis and evaluation have not been done. To do the performance evaluation for the dynamic workflow changes, comparison of the times (called change time) cost in the individual change and the methods how to obtain such times become ever important. In this paper, we first give a definition of change time and then propose the computation methods individually for each change type. Finally, we do experiments to evaluate the performance of three changes by doing the comparison of the change times.

This paper deals with two-processor scheduling for general acyclic SWITCH-less program nets with random node firing times. First, we introduce a hybrid priority list L* that has been shown to generate optimal schedules for the acyclic SWITCH-less program nets with unity node firing times, of which AND-nodes possess at most single input edge. Then considering the factors of existence of the AND-nodes with two input edges as well as random node firing times, we extend L* to design a new dynamic priority list Ld and four static priority lists {Lsii=1,2,3,4}; and then combining Ld and Lsi (i=1,2,3,4) we propose four hybrid priority lists {L*ii=1,2,3,4}. Finally, we apply genetic algorithm to evaluate the schedules generated by the four lists through simulations on 400 program nets. Our simulation results show two of the four lists can generate reasonably good schedules.

This paper discusses formal modeling and performance evaluation for a type of dynamic change of workflow, called Migrate. Workflow means the flow of work and is designed to process similar instances, called cases. Companies need to continuously refine their current workflow in order to adapt them to various requirements. The change of a current workflow is called dynamic change of the workflow. Before changing a workflow, there exist cases in the workflow. If these cases are ignored or fall into deadlock, the changed workflow would become inconsistent. Since Ellis et al. proposed three change types, Flush, Abort, and Synthetic Cut-Over that keep consistency of workflows in 1995, various change types have been proposed, in which there is a promising change type called Migrate that is proposed by Sadiq et al. Sadiq et al. proposed the concept of Migrate, but did not give a formal model of Migrate. Meanwhile, we have proposed a measure, called change time, in order to evaluate dynamic change of workflows, and used this measure to evaluate the performance on change time for Ellis et al. 's three change types. However, the performance evaluation on change time for Migrate has not been done. In this paper, we first give a Petri-nets-based model of Migrate. Then we present a method of computing change time based on the net model. Finally, we apply the method to 270 examples and show the comparison results between Migrate and Ellis et al. 's three change types.

This paper deals with the firing activities of a data-flow program net, which is extended from conventional data-flow graph by allowing edge thresholds α and β to be any positive integer number, while a conventional data-flow graph has αβ1. For a switchless program net, a necessary and sufficient condition of structural termination is shown and an algorithm for verifying structural termination is provided. For a program net with switches that change their states only once during whole program execution, a sufficient condition for the uniqueness of maximum firing numbers is given.

This paper deals with two-processor scheduling for a class of program nets, that are acyclic and SWITCH-less, and of which each node has unity node firing time. Firstly, we introduce a hybrid priority list L* that generates optimal schedules for the nets whose AND-nodes possess at most single input edge. Then we extend L* to suit for general program nets to give a new priority list L**. Finally, we use genetic algorithm to do the performance evaluation for the schedules generated by L** and show these schedules are quite close to optimal ones.

In this paper, we discuss a new property, named dead, of (dataflow) program nets. We say that a node of a program net is dead iff the node cannot fire once in any possible firing sequence, and furthermore the program net is partially dead. We tackle a problem of deciding whether a given program net is partially dead, named dead problem. Program nets can be classified into four subclasses: general, acyclic, SWITCH-less, and acyclic SWITCH-less nets. For each subclass, we give a method of solving dead problem and its computation complexity. Our results show that (i) acyclic SWITCH-less nets are not partially dead; (ii) for SWITCH-less nets, dead problem can be solved in polynomial time; (iii) for acyclic nets and general nets, dead problem is intractable.

A data-flow program net is a graph representation of data-flow programs consisting of three types of nodes, AND-node, OR-node and SWITCH-node, which represent arithmetic/logical, data merge and context switch operations respectively. Token self-cleanness is an important property of a data-flow program and is such that if date-flow programs satisfy the property then a date-flow computer can efficiently withdraw copies from given programs during executions. In this paper, we classify program nets into SWITCH-less, OR-less and general nets, and analyse structures of data-flow program nets to propose verification methods of token self-cleanness by investigating token numbers appearing on the edges. As a result, a necessary and sufficient condition is proposed for SWITCH-less data-flow program nets and sufficient conditions are given for OR-less and general data-flow program nets.