Graph models for reachability analysis of concurrent programs

Reachability analysis is an attractive technique for analysis of concurrent programs because it is simple and relatively straightforward to automate, and can be used in conjunction with model-checking procedures to check for application-specific as well as general properties. Several techniques have been proposed differing mainly on the model used; some of these propose the use of flowgraph based models, some others of Petri nets.This paper addresses the question: What essential difference does it make, if any, what sort of finite-state model we extract from program texts for purposes of reachability analysis? How do they differ in expressive power, decision power, or accuracy? Since each is intended to model synchronization structure while abstracting away other features, one would expect them to be roughly equivalent.We confirm that there is no essential semantic difference between the most well known models proposed in the literature by providing algorithms for translation among these models. This implies that the choice of model rests on other factors, including convenience and efficiency.Since combinatorial explosion is the primary impediment to application of reachability analysis, a particular concern in choosing a model is facilitating divide-and-conquer analysis of large programs. Recently, much interest in finite-state verification systems has centered on algebraic theories of concurrency. Yeh and Young have exploited algebraic structure to decompose reachability analysis based on a flowgraph model. The semantic equivalence of graph and Petri net based models suggests that one ought to be able to apply a similar strategy for decomposing Petri nets. We show this is indeed possible through application of category theory

Improving the Accuracy of Petri Net-based Analysis of Concurrent Programs

Spurious results are an inherent problem of most static analysis methods. These methods, in an effort to produce conservative results, overestimate the executable behavior of a program. Infeasible paths and imprecise alias resolution are the two causes of such inaccuracies. In this paper we present an approach for improving the accuracy of Petri net-based analysis of concurrent programs by including additional program state information in the Petri net. We present empirical results that demonstrate the improvements in accuracy and, in some cases, the reduction in the search space that result from applying this approach to concurrent Ada programs

Performance Bounds for Synchronized Queueing Networks

Las redes de Petri estocásticas constituyen un modelo unificado de las diferentes extensiones de redes de colas con sincronizaciones existentes en la literatura, válido para el diseño y análisis de prestaciones de sistemas informáticos distribuidos. En este trabajo se proponen técnicas de cálculo de cotas superiores e inferiores de las prestaciones de redes de Petri estocásticas en estado estacionario. Las cotas obtenidas son calculables en tiempo polinómico en el tamaño del modelo, por medio de la resolución de ciertos problemas de programación lineal definidos a partir de la matriz de incidencia de la red (en este sentido, las técnicas desarrolladas pueden considerarse estructurales). Las cotas calculadas dependen sólamente de los valores medios de las variables aleatorias que describen la temporización del sistema, y son independientes de los momentos de mayor orden. Esta independencia de la forma de las distribuciones de probabilidad asociadas puede considerarse como una útil generalización de otros resultados existentes para distribuciones particulares, puesto que los momentos de orden superior son, habitualmente, desconocidos en la realidad y difíciles de estimar. Finalmente, las técnicas desarrolladas se aplican al análisis de diferentes ejemplos tomados de la literatura sobre sistemas informáticos distribuidos y sistemas de fabricación. ******* Product form queueing networks have long been used for the performance evaluation of computer systems. Their success has been due to their capability of naturally expressing sharing of resources and queueing, that are typical situations of traditional computer systems, as well as to their efficient solution algorithms, of polynomial complexity on the size of the model. Unfortunately, the introduction of synchronization constraints usually destroys the product form solution, so that general concurrent and distributed systems are not easily studied with this class of models. Petri nets have been proved specially adequate to model parallel and distributed systems. Moreover, they have a well-founded theory of analysis that allows to investigate a great number of qualitative properties of the system. In the original definition, Petri nets did not include the notion of time, and tried to model only the logical behaviour of systems by describing the causal relations existing among events. This approach showed its power in the specification and analysis of concurrent systems in a way independent of the concept of time. Nevertheless the introduction of a timing specification is essential if we want to use this class of models for the performance evaluation of distributed systems. One of the main problems in the actual use of timed and stochastic Petri net models for the quantitative evaluation of large systems is the explosion of the computational complexity of the analysis algorithms. In general, exact performance results are obtained from the numerical solution of a continuous time Markov chain, whose dimension is given by the size of the state space of the model. Structural computation of exact performance measures has been possible for some subclasses of nets such as those with state machine topology. These nets, under certain assumptions on the stochastic interpretation are isomorphic to Gordon and Newell's networks, in queueing theory terminology. In the general case, efficient methods for the derivation of performance measures are still needed. Two complementary approaches to the derivation of exact measures for the analysis of distributed systems are the utilization of approximation techniques and the computation of bounds. Approximate values for the performance parameters are in general more efficiently derived than the exact ones. On the other hand, "exactness" only exists in theory! In other words, numerical algorithms must be applied in practice for the computation of exact values, therefore making errors is inevitable. Performance bounds are useful in the preliminary phases of the design of a system, in which many parameters are not known accurately. Several alternatives for those parameters should be quickly evaluated, and rejected those that are clearly bad. Exact (and even approximate) solutions would be computationally very expensive. Bounds become useful in these instances since they usually require much less computation effort. The computation of upper and lower bounds for the steady-state performance of timed and stochastic Petri nets is considered in this work. In particular, we study the throughput of transitions, defined as the average number of firings per time unit. For this measure we try to compute upper and lower bounds in polynomial time on the size of the net model, by means of proper linear programming problems defined from the incidence matrix of the net (in this sense, we develop structural techniques). These bounds depend only on the mean values and not on the higher moments of the probability distribution functions of the random variables that describe the timing of the system. The independence of the probability distributions can be viewed as a useful generalization of the performance results, since higher moments of the delays are usually unknown for real cases, and difficult to estimate and assess. From a different perspective, the obtained results can be applied to the analysis of queueing networks extended with some synchronization schemes. Monoclass queueing networks can be mapped on stochastic Petri nets. On the other hand, stochastic Petri nets can be interpreted as monoclass queueing networks augmented with synchronization primitives. Concerning the presentation of this manuscript, it should be mentioned that chapter 1 has been written with the object of giving the reader an outline of the stochastic Petri net model: its definition, terminology, basic properties, and related concepts, together with its deep relation with other classic stochastic network models. Chapter 2 is devoted to the presentation of the net subclasses considered in the rest of the work. The classification presented here is quite different from the one which is usual in the framework of Petri nets. The reason lies on the fact that our classification criterion, the computability of visit ratios for transitions, is introduced for the first time in the field of stochastic Petri nets in this work. The significance of that criterion is based on the important role that the visit ratios play in the computation of upper and lower bounds for the performance of the models. Nevertheless, classical important net subclasses are identified here in terms of the computability of their visit ratios from different parameters of the model. Chapter 3 is concerned with the computation of reachable upper and lower bounds for the most restrictive subclass of those presented in chapter 2: marked graphs. The explanation of this fact is easy to understand. The more simple is the model the more accessible will be the techniques an ideas for the development of good results. Chapter 4 provides a generalization for live and bounded free choice nets of the results presented in the previous chapter. Quality of obtained bounds is similar to that for strongly connected marked graphs: throughput lower bounds are reachable for bounded nets while upper bounds are reachable for 1-bounded nets. Chapter 5 considers the extension to other net subclasses, like mono-T-semiflow nets, FRT-nets, totally open deterministic systems of sequential processes, and persistent nets. The results are of diverse colours. For mono-T-semiflow nets and, therefore, for general FRT-nets, it is not possible (so far) to obtain reachable throughput bounds. On the other hand, for bounded ordinary persistent nets, tight throughput upper bounds are derived. Moreover, in the case of totally open deterministic systems of sequential processes the exact steady-state performance measures can be computed in polynomial time on the net size. In chapter 6 bounds for other interesting performance measures are derived from throughput bounds and from classical queueing theory laws. After that, we explore the introduction of more information from the probability distribution functions of service times in order to improve the bounds. In particular, for Coxian service delay of transitions it is possible to improve the throughput upper bounds of previous chapters which held for more general forms of distribution functions. This improvement shows to be specially fruitful for live and bounded free choice nets. Chapter 7 is devoted to case studies. Several examples taken from literature in the fields of distributed computing systems and manufacturing systems are modelled by means of stochastic Petri nets and evaluated using the techniques developed in previous chapters. Finally, some concluding remarks and considerations on possible extensions of the work are presented

A Colored Petri Net-Based Approach for Automated Deadlock Detection in Parallel Programs

A static analysis approach is proposed for automated detection of deadlocks in a common class of parallel programs, referred to as Single Code Multiple Data (SCMD) programs. It is based on colored Petri net (CP-net) modeling and reachability analysis, where colors correspond to parallel processes. An SCMD program is first translated into a CP-net and a reachability tree is then derived and analyzed for deadlock information. CP-subnets representing basic programming language constructs are described. These subnets are employed as building blocks by an algorithm that translates synchronization-related statements of a process in an SCMD program and connects the resulting subnets. The connection technique makes use of the characteristics of SCMD programs to produce a unified and folded CP-net model. These characteristics are also used to introduce a notion, referred to as poset-covering, that leads to a reduced reachability tree for the Cp-net. The usual algorithm for generating and analyzing reachability trees of CP-nets is modified by including poset-covering and excluding notions that are irrelevant to our application. The compactness of the CP-net model and the reachability tree makes the proposed approach appealing for practical implementation

A formal approach to AADL model-based software engineering

Formal methods have become a recommended practice in safety-critical software engineering. To be formally verified, a system should be specified with a specific formalism such as Petri nets, automata and process algebras, which requires a formal expertise and may become complex especially with large systems. In this paper, we report our experience in the formal verification of safety-critical real-time systems. We propose a formal mapping for a real-time task model using the LNT language, and we describe how it is used for the integration of a formal verification phase in an AADL model-based development process. We focus on real-time systems with event-driven tasks, asynchronous communication and preemptive fixed-priority scheduling. We provide a complete tool-chain for the automatic model transformation and formal verification of AADL models. Experimentation illustrates our results with the Flight control system and Line follower robot case studies

Software Engineering and Petri Nets

This booklet contains the proceedings of the Workshop on Software Engineering and Petri Nets (SEPN), held on June 26, 2000. The workshop was held in conjunction with the 21st International Conference on Application and Theory of Petri Nets (ICATPN-2000), organised by the CPN group of the Department of Computer Science, University of Aarhus, Denmark. The SEPN workshop papers are available in electronic form via the web page:http://www.daimi.au.dk/pn2000/proceeding

Translating expert system rules into Ada code with validation and verification

The purpose of this ongoing research and development program is to develop software tools which enable the rapid development, upgrading, and maintenance of embedded real-time artificial intelligence systems. The goals of this phase of the research were to investigate the feasibility of developing software tools which automatically translate expert system rules into Ada code and develop methods for performing validation and verification testing of the resultant expert system. A prototype system was demonstrated which automatically translated rules from an Air Force expert system was demonstrated which detected errors in the execution of the resultant system. The method and prototype tools for converting AI representations into Ada code by converting the rules into Ada code modules and then linking them with an Activation Framework based run-time environment to form an executable load module are discussed. This method is based upon the use of Evidence Flow Graphs which are a data flow representation for intelligent systems. The development of prototype test generation and evaluation software which was used to test the resultant code is discussed. This testing was performed automatically using Monte-Carlo techniques based upon a constraint based description of the required performance for the system

The Impact of Petri Nets on System-of-Systems Engineering

The successful engineering of a large-scale system-of-systems project towards deterministic behaviour depends on integrating autonomous components using international communications standards in accordance with dynamic requirements. To-date, their engineering has been unsuccessful: no combination of top-down and bottom-up engineering perspectives is adopted, and information exchange protocol and interfaces between components are not being precisely specified. Various approaches such as modelling, and architecture frameworks make positive contributions to system-of-systems specification but their successful implementation is still a problem. One of the most popular modelling notations available for specifying systems, UML, is intuitive and graphical but also ambiguous and imprecise. Supplying a range of diagrams to represent a system under development, UML lacks simulation and exhaustive verification capability. This shortfall in UML has received little attention in the context of system-of-systems and there are two major research issues: 1. Where the dynamic, behavioural diagrams of UML can and cannot be used to model and analyse system-of-systems 2. Determining how Petri nets can be used to improve the specification and analysis of the dynamic model of a system-of-systems specified using UML This thesis presents the strengths and weaknesses of Petri nets in relation to the specification of system-of-systems and shows how Petri net models can be used instead of conventional UML Activity Diagrams. The model of the system-of-systems can then be analysed and verified using Petri net theory. The Petri net formalism of behaviour is demonstrated using two case studies from the military domain. The first case study uses Petri nets to specify and analyse a close air support mission. This case study concludes by indicating the strengths, weaknesses, and shortfalls of the proposed formalism in system-of-systems specification. The second case study considers specification of a military exchange network parameters problem and the results are compared with the strengths and weaknesses identified in the first case study. Finally, the results of the research are formulated in the form of a Petri net enhancement to UML (mapping existing activity diagram elements to Petri net elements) to meet the needs of system-of-systems specification, verification and validation