Fuzzy rule base systems verification using high-level Petri nets

In this paper, we propose a Petri nets formalism for the verification of rule-based systems. Typical structural errors in a rule-based system are redundancy, inconsistency, incompleteness, and circularity. Since our verification is based on Petri nets and their incidence matrix, we need to transform rules into a Petri nets first, then derive an incidence matrix from the net. In order to let fuzzy rule-based systems detect above the structural errors, we are presenting a Petri-nets-based mechanism. This mechanism consists of three phases: rule normalization, rules transformation, and rule verification. Rules will be first normalized into Horn clauses, then transform the normalized rules into a high-level Petri net, and finally we verify these normalized rules. In addition, we are presenting our approach to simulate the truth conditions which still hold after a transition firing and negation in Petri nets for rule base modeling. In this paper, we refer to fuzzy rules as the rules with certainty factors, the degree of truth is computed in an algebraic form based on state equation which can be implemented in matrix computation in Petri nets. Therefore, the fuzzy reasoning problems can be transformed as the liner equation problems that can be solved in parallel. We have implemented a Petri nets tool to realize the mechanism presented fuzzy rules in this paper.     

System modelling with high-level Petri nets

The paper presents a high-level Petri net model of concurrent systems called predicate /transition-nets (PrT-nets). Its places represent variable properties of, or relations between, individuals; they are ‘predicates’ with variable extension. The transitions represent classes of elementary changes of those extensions. The model is introduced on the basis of a simple example from resource management. The central part of the paper is devoted to linear-algebraic techniques for verifying invariant assertions, yielding a calculus of S-invariants for PrT-nets. Finally, these modelling and analysis techniques are applied to a scheme for organizing a distributed data base taken from literature.     

Reinforcement learning for high-level fuzzy Petri nets

The author has developed a reinforcement learning algorithm for the high-level fuzzy Petri net (HLFPN) models in order to perform structure and parameter learning simultaneously. In addition to the HLFPN itself, the difference and similarity among a variety of subclasses concerning Petri nets are also discussed. As compared with the fuzzy adaptive learning control network (FALCON), the HLFPN model preserves the advantages that: 1) it offers more flexible learning capability because it is able to model both IF-THEN and IF-THEN-ELSE rules; 2) it allows multiple heterogeneous outputs to be drawn if they exist; 3) it offers a more compact data structure for fuzzy production rules so as to save information storage; and 4) it is able to learn faster due to its structural reduction. Finally, main results are presented in the form of seven propositions and supported by some experiments.     

A methodology of testing high-level Petri nets

Petri nets have been extensively used in the modelling and analysis of concurrent and distributed systems. The verification and validation of Petri nets are of particular importance in the development of concurrent and distributed systems. As a complement to formal analysis techniques, testing has been proven to be effective in detecting system errors and is easy to apply. An open problem is how to test Petri nets systematically, effectively and efficiently. An approach to solve this problem is to develop test criteria so that test adequacy can be measured objectively and test cases can be generated efficiently, even automatically. In this paper, we present a methodology of testing high-level Petri nets based on our general theory of testing concurrent software systems. Four types of testing strategies are investigated, which include state-oriented testing, transition-oriented testing, flow-oriented testing and specification-oriented testing. For each strategy, a set of schemes to observe and record testing results and a set of coverage criteria to measure test adequacy are defined. The subsumption relationships and extraction relationships among the proposed testing methods are systematically investigated and formally proved.     

A reasoning algorithm for high-level fuzzy Petri nets

We introduce an automated procedure for extracting information from knowledge bases that contain fuzzy production rules. The knowledge bases considered here are modeled using the high-level fuzzy Petri nets proposed by the authors in the past. Extensions to the high-level fuzzy Petri net model are given to include the representation of partial sources of information. The case of rules with more than one variable in the consequent is also discussed. A reasoning algorithm based on the high-level fuzzy Petri net model is presented. The algorithm consists of the extraction of a subnet and an evaluation process. In the evaluation process, several fuzzy inference methods can be applied. The proposed algorithm is similar to another procedure suggested by Yager (1983), with advantages concerning the knowledge-base searching when gathering the relevant information to answer a particular kind of query     

Modeling and verification of the SDL-specified communication protocols using high-level Petri nets

To simplify modeling and verification of communication protocols presented in the SDL language, the so-called hierarchical typed timed Petri nets (HTT nets), which are substantial modifications of colored Petri nets, are introduced. A method of translation of the SDL language into HTT nets is described. A program complex SPV (SDL Protocol Verifier), which includes a translator from SDL into HTT nets and means for editing, simulation, visualization, and verification of these net models, is presented. For the verification, a model checking method for properties presented by μ-calculus formulas is used. Experiments on application of the SPV complex for modeling and verifying two ring protocols (RE and ATMR protocols), an optimized version of the sliding window protocol (i-protocol), and a dynamic version of the InRes protocol are described     

Distributed dynamic programming using concurrent object-orientedness with actors visualized by high-level Petri nets

This paper deals with application of concurrent object-oriented programming with Actors to solve dynamic programming problems in a distributed computing environment. This area of research is often called distributed artificial intelligence. Using a dynamic programming example of chained matrix multiplication, a method of managing dynamic programming searches in a distributed programming environment with Actors is presented. Distributed computations with Actors are visualized by means of Time-Varying Automata (for cases with no intra-actor concurrency) or using a class of high-level nets called Hierarchical Colored Petri Nets (for cases with intra-actor concurrency). Design and implementation features of the specific Actor-based programming environment, using a concurrent extension of C++, are also discussed.     

Application of high-level fuzzy Petri nets to educational grading system

For the purpose of understanding the students’ learning achievement, the most direct way is to implement a test. Due to the rapid development of information technology, all kinds of combination of information technology with the adaptive test have been incessantly noted by many scholars. In general, the computerized adaptive test includes the item response theory that tests the students’ learning ability of subjects. However, the results based only on the dichotomy of correct answers and wrong answers are not so comprehensive judgments. Situations of correct answers and wrong answers should be different in their degrees; for example, completely correct, partially correct, completely wrong, and partially wrong. But the partially correct or partially wrong is vague and difficult to define. Thus it is appropriate to use fuzzy theory to solve the vagueness problem. Therefore, this study presents a novel learning evaluation model which applies high-level fuzzy Petri net (HLFPN) and infers via a fuzzy reasoning method the different answering performances generated by different examinee’s abilities corresponding to the test items in different degrees of difficulty. Finally, we synthesize the answering performance of every test item and make a reasonable evaluation.     

基于对象的扩展Petri网协同设计过程分析

针对协同设计中任务的执行流程缺乏柔性,不利于分析实际设计过程的现状,提出一种单元调用变迁对与决策变迁相集成的基于对象的扩展Petri网,扩展了Petri网的可达图以适应分析OEPNs模型.采用OEPNs中的过程网和单元阿对协同设计过程楚模,利用模型中的单元调用变迁对和决策变迁对过程本身和可能状态进行分析.最后与相关的研究工作进行比较并给出了结论.     

A simplification of a conversation design scheme using Petri nets

In the conversation design procedure, the definition of the state of the system is one of the most important aspects. The question is how to identify transitions in Occam programs in order to express them as Petri nets. In the paper, a simplified transition identification method is proposed. Using the robot arm control program of A.M. Tyrrell and D.J. Holding it is shown that the correspondent Petri net graph is simpler than theirs, but the communication state change table is the same. It is also shown that these two methods are equivalent     

Performance analysis using Petri nets

The purpose of this paper is to focus on the implementation issues associated with using Petri nets for the performance analysis of discrete event dynamic systems while demonstrating several applications in manufacturing systems. Practical modeling issues will be discussed and several applications will be presented that illustrate the advantages and limitations of this methodology. These issues lead to the definition of several research problems in Petri nets for performance analysis.     

Timed high-level nets

Petri nets have been widely used for modeling and analyzing concurrent systems. Several reasons contribute to their success: the simplicity of the model, the immediate graphical representation, the easy modeling of asynchronous aspects, the possibility of reasoning about important properties such as reachability, liveness, boundedness. However, the original model fails in representing two important features: complex functional aspects, such as conditions which rule the flow of control, and time. Due to that, two different classes of extensions of Petri nets have been proposed: high-level nets and timed Petri nets. High-level nets allow the representation of functional aspects in full details, but do not provide a means for representing time; on the other hand, timed Petri nets have been thought for time representation, but they do not provide a means for representing detailed functinal aspects. Thus, these two important aspects cannot be mastered together. In particular, it is difficult to express relationships between time and functional aspects.This paper investigates the relationships between high-level nets and timed Petri nets, thus extending a first set of results published in a previous paper, where a unifying Petri net based model for time representation has been proposed. It first recalls how time can be represented in a Petri net extension called ER nets, and assesses its generality. It then investigates the relationships of ER nets with the best known high-level nets. In particular it shows the overall equivalence of ER nets, Colored Petri nets and Predicate/Transition nets, and extends the mechanism for time representation introduced in ER nets to both Colored Petri nets and Predicate/Transition nets. It also shows that these models cannot be simplified without significantly constraining the timing aspects that can be modeled.     

随机Petri网在框架设计中的应用

为了实现系统框架的良好设计和高效性能,研究了随机Petri网的选择、串联、并联和循环4种基本模型的性能计算方法.以数字化档案管理系统为具体实例,根据框架的各项性能要求,对档案数字化的过程进行了基于随机Petri网的建模分析和计算.实验结果表明,随机Petri网在框架的设计过程中起到了重要的作用,有效地指导了框架的设计和性能的优化.     

Parallel computation of continuous Petri nets based on hypergraph partitioning

Continuous Petri net can be used for performance analysis or static analysis. The analysis is based on solving the associated ordinary differential equations. This paper presents a method to parallel compute these differential equations. We first map the Petri net to a hypergraph, and then partition the hypergraph to minimize interprocessor communication while maintaining a good load balance; Based on the partition result, we divide the differential equations into several blocks; Finally, we design a parallel computing algorithm to compute these equations. Software hMETIS is used to partition the hypergraph, and software SUNDIALS is used to support the parallel computing of differential equations. Gas station problem and dining philosopher problem have been used to demonstrate the feasibility, accuracy, and scalability of our method.     

Fuzzy backward reasoning using fuzzy Petri nets

Chen, Ke and Chang (1990) have presented a fuzzy forward reasoning algorithm for rule-based systems using fuzzy Petri nets. In this paper, we extend the work of Chen, Ke and Chang (1990) to present a fuzzy backward reasoning algorithm for rule-based systems using fuzzy Petri nets, where the fuzzy production rules of a rule-based system are represented by fuzzy Petri nets. The system can perform fuzzy backward reasoning automatically to evaluate the degree of truth of any proposition specified by the user. The fuzzy backward reasoning capability allows the computers to perform reasoning in a more flexible manner and to think more like people.     

Giving semantics to SA/RT by means of high-level timed Petri nets

In the IPTES project a dual language approach is proposed for overcoming both the problems derived from the use of a user-friendly, high-level, but not-formally-defined language and from a lower-level, formal, but difficult-to-use language. The approach uses a user-friendly, high-level language as user interface and a lower-level, formal language asmachine language. In this way the users can both access the IPTES environment through a nice interface and can profit from non-ambiguity-checks and proofs algorithms based on the formal kernel machine language. The correspondence between the two languages is built-in in the IPTES environment that provides a transparent mapping mechanism that relates the users specifications expressed by means of the high-level interface-language with the formal definitions expressed in the formal machine language.This paper presents the mapping mechanism that relates the current IPTES user interface (SA/RT (Ward and Mellor 1985)) with the IPTES machine language (high-level timed Petri nets (Ghezzi, Mandrioli, Morasca and Pezzé 1991)). As a side effect, it also presents the formal semantics of SA/RT defined by means of high-level timed Petri nets.This material is based upon work supported by the CEC under the ESPRIT program project no. EP5570 IPTES, by the Piano Finalizzato Sistemi Informatici e Calcolo Parallelo (CNR) and by The Technical Development Centre of Finland (TEKES).     

Designing an asynchronous processor using Petri nets

Using a simple example, we demonstrate how to design and analyze asynchronous systems from labeled Petri net specifications, later refining, transforming, and translating them for implementations