A new approach to verify rule-based systems using petri nets

In the past several years, various graphical techniques were proposed to analyze various types of structural errors, including inconsistency (conflict rules), incompleteness (missing rules), redundancy (redundant rules), and circularity (circular depending rules), in rule-based systems in which rules can be represented in propositional logic. In this paper, we present a special reachability graph technique based on ω-nets (a special type of low-level petri nets) to detect all of the above types of structural errors. Our new technique is simple, efficient, and can be easily automated. We highlight the unique features of this new approach and demonstrate its application through two examples.     

Verification of problem-based learning systems using modified petri nets

In this paper, we intend to verify a web-based system on problem-based learning (PBL). To consider the design flow of the web-based PBL system, it is essential to avoid the potential hazard introduced by a logically incorrect system design. In order to eliminate the potential hazard, we define a new class of Petri net, namely, an Activity Flow (AF) net, which is suitable to be converted from a UML (Unified Modeling Language) activity diagram. Through the siphon-based deadlock detection of the AF net, we can find whether there is a process hazard in the UML activity diagram or not. This is helpful to implement the PBL system and to ensure the correct activities and the right control flow. In addition, we attempt to enhance the quality of the system verification by using a questionnaire. Thus we can interpret the user’s level of satisfaction with the designed PBL system. These two verification approaches bring us to achieve an adequately positive response to the web-based PBL system.     

Modelling automated manufacturing systems using a modification of coloured petri nets

Automated manufacturing systems (AMS) are a class of systems exhibiting concurrency, asynchronicity and distributedness, and can be modelled using Petri nets. The advantage of using Petri nets is that they provide graphical models, with formal methods of analysis. However, graphical representation of Petri net models becomes difficult even for medium-sized systems since such graphs tend to become inconveniently large. Coloured Petri nets (CPN) are a variant which enables a more concise representation with the same modelling power. This paper develops a model for simulation of AMS whose correctness can be formally established, and which can be graphically represented and visually understood. It presents a modelling approach for AMS, based on a modified version of CPN, with enhanced modelling power. The proposed modifications result in highly compact graphical representations, and also render the model dynamic, i.e. capable of changing dynamically to reflect currently selected system parameters. These features make the proposed model ideally suited for discrete event simulation.     

Verification of causal models using petri nets

Many different approaches, mainly based on logical formalisms, have been proposed for modeling causal knowledge and the inferential mechanisms based on this type of knowledge. In this article we present an alternative approach to this problem in which the semantics of a causal model is provided by adopting Petri nets. We show how this scheme of modeling is powerful enough to capture all crucial aspects of the corresponding causal model, without resorting to very complex structures; indeed, the model is obtained using a particular type of deterministic Petri net. Moreover, a complete formalization of the aspects concerning the correctness of the represented causal model is provided in terms of reachability in the Petri net. We believe that this aspect is very important in the knowledge acquisition phase when precise correctness criteria should be defined and respected in the construction of the model. We analyze some of these criteria and we discuss an algorithm (based on a backward simulation of the net) capable of discovering incorrectness by exploiting analysis tools available for Petri nets and the explicit parallelism of the model. © 1992 John Wiley & Sons, Inc.     

Specification of software pipelining using petri nets

This paper presents a flexible model for software pipelining using the petri nets. Our technique, called the Petri Net Pacemaker (PNP), can create near optimal pipelines with less algorithmic effort than other techniques. The pacemaker is a novel idea which exploits the cyclic behavior of petri nets to model the problem of scheduling operations of a loop body for software pipelining. A way of improving the performance of loops containing predicates is given. The PNP technique also shows how nested loops can be pipelined. A comparison with some of the other techniques is presented. THis work was partially supported by the National Science Foundation under grants CDA-9100788 and CDA-9200371.     

Analysis of multi-agent activity using petri nets

This paper presents the use of place/transition petri nets (PNs) for the recognition and evaluation of complex multi-agent activities. The PNs were built automatically from the activity templates that are routinely used by experts to encode domain-specific knowledge. The PNs were built in such a way that they encoded the complex temporal relations between the individual activity actions. We extended the original PN formalism to handle the propagation of evidence using net tokens. The evaluation of the spatial and temporal properties of the actions was carried out using trajectory-based action detectors and probabilistic models of the action durations. The presented approach was evaluated using several examples of real basketball activities. The obtained experimental results suggest that this approach can be used to determine the type of activity that a team has performed as well as the stage at which the activity ended.     

Modelling real world industrial systems: an inter-disciplinary approach based on petri nets

A modelling approach that will facilitate an in-depth understanding of the inter-relations of the different phenomena, human interactions and environmental factors constituting “real world” industrial processes is presented. Important industrial systems such as aluminium smelters, nuclear plants and batch chemical reactors have inter-related internal process activities coexisting with external events and requires an inter-disciplinary approach to model them. This modelling framework is based on identifying as modules, processes prevalent in industrial systems which to some degree are homogeneous in their actions. The selected initial set of modules are structured as petri net models and made to interact iteratively to provide process states of the system. The goal is accomplished by identifying the evolution of the process states and interpreting this in a markov chain as a means of effective representation of the “actual running” of the industrial process. The paper discusses the function and the implementation of the modelling method as applicable to the industrial reduction (smelting) of aluminium.     

Enzymatic competition: Modeling and verification with timed hybrid petri nets

The formalism of hybrid functional petri nets (HFPN) has proved its convenience for simulating biological systems. The drawback of the noticeable expressiveness of HFPN is the difficulty to perform formal verifications of dynamical properties. In this article, we propose a model-checking procedure for timed hybrid petri nets (THPN), a sub-class of HFPN. This procedure is based on the translation of the THPN model and of the studied property into real-time automata. It is applied to model enzymatic competitions existing in amphibian metamorphosis.     

Uncertainty management in expert systems using fuzzy Petri nets

The paper aims at developing new techniques for uncertainty management in expert systems for two generic class of problems using fuzzy Petri nets that represent logical connectivity among a set of imprecise propositions. One class of problems deals with the computation of fuzzy belief of any proposition from the fuzzy beliefs of a set of independent initiating propositions in a given network. The other class of problems is concerned with the computation of steady-state fuzzy beliefs of the propositions embedded in the network, from their initial fuzzy beliefs through a process called belief revision. During belief revision, a fuzzy Petri net with cycles may exhibit “limit cycle behavior” of fuzzy beliefs for some propositions in the network. No decisions can be arrived at from a fuzzy Petri net with such behavior. To circumvent this problem, techniques have been developed for the detection and elimination of limit cycles. Further, an algorithm for selecting one evidence from each set of mutually inconsistent evidences, referred to as nonmonotonic reasoning, has also been presented in connection with the problems of belief revision. Finally, the concepts proposed for solving the problems of belief revision have been applied successfully for tackling imprecision, uncertainty, and nonmonotonicity of evidences in an illustrative expert system for criminal investigation     

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.     

An approach to systems verification

The term systems verification refers to the specification and verification of the components of a computing system, including compilers, assemblers, operating systems and hardware. We outline our approach to systems verification, and summarize the application of this approach to several systems components. These components consist of a code generator for a simple high-level language, an assembler and linking loader, a simple operating system kernel, and a microprocessor design.     

Decision support systems: An expert systems approach

This paper provides a conceptual framework for designing decision support systems (DSS) using an expert systems approach. Currently there is a significant trend towards the use of knowledge-based systems techniques in DSS design, but a comprehensive framework is yet to be proposed. Our paper addresses this problem and presents such a framework. Efforts are currently underway to design, implement and test a system based on this framework.     

Specification and performance analysis of embedded systems with coloured petri nets

To analyze synchronization, concurrency, communication protocols and system performance, a system level specification is modelled in a coloured Petri net. A toolbox collects information for the implementation, e.g., processing times, waiting times, idle times, data accesses, processing requests. This is illustrated with a data-link protocol system, where the disturbance on the communication channels is modelled, too.     

A new methodology for analyzing distributed systems modeled by petri nets

Distributed computing systems can be modeled adequately by Petri nets. The computation of invariants of Petri nets becomes necessary for proving the properties of modeled systems. This paper presents a two-phase, bottom-up approach for invariant computation and analysis of Petri nets. In the first phase, a newly defined subnet, called the RP-subnet, with an invariant is chosen. In the second phase, the selected RP-subnet is analyzed. Our methodology is illustrated with two examples viz., the dining philosophers' problem and the connection-disconnection phase of a transport protocol. We believe that this new method, which is computationally no worse than the existing techniques, would simplify the analysis of many practical distributed systems.     

Design of industrial regulators using expert systems approach

The applicability of the expert system approach to the design of industrial regulators is demonstrated. A brief overview of an expert system, CONEX, has been presented first. The result of applying CONEX to solve two industrial regulation problems is then discussed. The designs obtained by CONEX have been compared with those obtained through ‘non-expert-system’ approach.     

An approach to the numerical verification of solutions for obstacle problems

In this paper, we consider numerical techniques which enable us to verify the existence of solutions for a general obstacle problem using computers. We describe the numerical verification algorithm for solving a two dimensional obstacle problem and report a numerical result.