Commodification of accelerations for the Karp and Miller Construction

Karp and Miller’s algorithm is based on an exploration of the reachability tree of a Petri net where, the sequences of transitions with positive incidence are accelerated. The tree nodes of Karp and Miller are labeled with ω-markings representing (potentially infinite) coverability sets. This set of ω-markings allows us to decide several properties of the Petri net, such as whether a marking is coverable or whether the reachability set is finite. The edges of the Karp and Miller tree are labeled by transitions but the associated semantic is unclear which yields to a complex proof of the algorithm correctness. In this work we introduce three concepts: abstraction, acceleration and exploration sequence. In particular, we generalize the definition of transitions to ω-transitions in order to represent accelerations by such transitions. The notion of abstraction makes it possible to greatly simplify the proof of the correctness. On the other hand, for an additional cost in memory, which we theoretically evaluated, we propose an “accelerated” variant of the Karp and Miller algorithm with an expected gain in execution time. Based on a similar idea we have accelerated (and made complete) the minimal coverability graph construction, implemented it in a tool and performed numerous promising benchmarks issued from realistic case studies and from a random generator of Petri nets.

     

Liveness-enforcing supervision of bounded ordinary Petri nets usingpartial order methods

This paper combines and refines recent results into a systematic way to verify and enforce the liveness of bounded ordinary Petri nets. The approach we propose is based on a partial-order method called network unfolding. Network unfolding maps the original Petri net to an acyclic occurrence net. A finite prefix of the occurrence net is defined to give a compact representation of the original net reachability graph while preserving the causality between net transitions. A set of transition invariants denoted as base configurations is identified in the finite prefix. These base configurations capture all of the fundamental executions of the net system, thereby providing a modular way to verify and synthesize supervisory net systems. This paper proves necessary and sufficient conditions that characterize the original net liveness and the existence of maximally permissive supervisory policies that enforce liveness     

Model-based testing for concurrent systems: unfolding-based test selection

Model-based testing has mainly focused on models where concurrency is interpreted as interleaving (like the ioco theory for labeled transition systems), which may be too coarse when one wants concurrency to be preserved in the implementation. In order to test such concurrent systems, we choose to use Petri nets as specifications and define a concurrent conformance relation named co-ioco. We present a test generation algorithm based on Petri net unfolding able to build a complete test suite w.r.t our co-ioco conformance relation. In addition, we propose several coverage criteria that allow to select finite prefixes of an unfolding in order to build manageable test suites.     

Petri网的反向展开及其在程序数据竞争检测的应用

展开技术借助分支进程可在一定程度上缓解Petri网性质分析中的状态爆炸问题.但展开网中仍然包含了系统的所有状态信息.某些应用问题仅需对系统特定状态的可覆盖性进行判定,以此为目标有望缩减网系统展开的规模.为此,本文针对安全Petri网的可覆盖性判定问题提出了一种目标导向的反向展开算法,结合启发式技术缩减展开的规模,以此提高目标标识可覆盖性判定的效率.进而,将反向展开算法应用于并发程序的形式化验证,将并发程序的数据竞争检测问题转换为Petri网特定标识的可覆盖性判定问题.实验对比了正向展开与反向展开在Petri网可覆盖性判定问题上的效率,结果表明,当Petri网展开的正向分支较多时,反向展开相比正向展开具有更高的可覆盖性判定效率.最后,本文对影响反向展开效率的关键因素做了分析与总结.     

Symbolic unfolding of parametric stopwatch Petri nets

We address the problem of unfolding safe parametric stopwatch time Petri nets (PSwPNs), i.e., safe time Petri nets (TPNs) possibly extended with time parameters and stopwatches. We extend the notion of branching process to account for the dates of the occurrences of events and thus define a symbolic unfolding for PSwPNs. In the case of TPNs we also propose a method based on our so-called time branching processes to compute a finite complete prefix of the symbolic unfolding. The originality of our work relies on a precise handling of direct conflicts between events, and the analysis of their effects on the constraints between the firing dates of those events.     

Verification of bounded Petri nets using integer programming

Model checking based on the causal partial order semantics of Petri nets is an approach widely applied to cope with the state space explosion problem. One of the ways to exploit such a semantics is to consider (finite prefixes of) net unfoldings—themselves a class of acyclic Petri nets—which contain enough information, albeit implicit, to reason about the reachable markings of the original Petri nets. In [19], a verification technique for net unfoldings was proposed, in which deadlock detection was reduced to a mixed integer linear programming problem. In this paper, we present a further development of this approach. The essence of the proposed modifications is to transfer the information about causality and conflicts between the events involved in an unfolding, into a relationship between the corresponding integer variables in the system of linear constraints. Moreover, we present some problem-specific optimisation rules, reducing the search space. To solve other verification problems, such as mutual exclusion or marking reachability and coverability, we adopt Contejean and Devie's algorithm for solving systems of linear constraints over the natural numbers domain and refine it, by taking advantage of the specific properties of systems of linear constraints to be solved. Another contribution of this paper is a method of re-formulating some problems specified in terms of Petri nets as problems defined for their unfoldings. Using this method, we obtain a memory efficient translation of a deadlock detection problem for a safe Petri net into an LP problem. We also propose an on-the-fly deadlock detection method. Experimental results demonstrate that the resulting algorithms can achieve significant speedups.

Branching processes of Petri nets

Summary The notion of a branching process is introduced, as a formalization of an initial part of a run of a Petri net, including nondeterministic choices. This generalizes the notion of a process in a natural way. It is shown that the set of branching processes of a Petri net is a complete lattice, with respect to the natural notion of partial order. The largest element of this lattice is the unfolding of the Petri net.     

On the well-foundedness of adequate orders used for construction of complete unfolding prefixes

Petri net unfolding prefixes are an important technique for formal verification and synthesis of concurrent systems. In this paper we show that the requirement that the adequate order used for truncating a Petri net unfolding must be well-founded is superfluous in many important cases, i.e., it logically follows from other requirements. We give a complete analysis when this is the case. These results concern the very ‘core’ of the unfolding theory.     

A graph-theoretic characterization theorem for multiplicative fragment of non-commutative linear logic

It is well known that every proof net of a non-commutative version of MLL (multiplicative fragment of commutative linear logic) can be drawn as a plane Danos–Regnier graph (drawing) satisfying the switching condition of Danos–Regnier [3]. In this paper, we study the reverse direction; we introduce a system MNCLL which is logically equivalent to the multiplicative fragment of cyclic linear logic introduced by Yetter [9], and show that any plane Danos–Regnier graph drawing with one terminal edge satisfying the switching condition represents a unique non-commutative proof net (i.e., a proof net of MNCLL). In the course of proving this, we also give the characterization of the non-commutative proof nets by means of the notion of strong planarity, as well as the notion of a certain long-trip condition, called the stack-condition, of a Danos–Regnier graph, the latter of which is related to Abrusci's balanced long-trip condition [2].     

Petri网展开图法的分析和应用

Petri网的展开图是一种特殊的并发系统状态空间搜索方法，它不需要重复考虑并发事件的所有可能的交集，从而大大缩减状态空间爆炸给验证分析带来的空间复杂度和时间复杂度。使用展开图分析Petri网的行为属性与传统的Petri网分析方法相比，具有自己的特点。该文首先介绍了Petri网展开图的构造算法，在此基础上使用展开图分析方法对一个典型Petri网的活性，有界性和可逆性等行为属性进行了分析，并与传统的Petri网分析方法作比较。     

Reverse Unfolding of Petri Nets and its Application in Program Data Race Detection

The unfolding technique can partially alleviate the state explosion in Petri nets through branching processes. However, all states of a system are still contained in its unfolding net. To deal with some practical problems, only the coverability determination of a specific state is needed. In view of this, reducing the scale of the unfolding net is feasible. This study proposes a target-oriented reverse unfolding algorithm for the coverability determination of 1-safe Petri nets, which combines a heuristic technique to reduce the scale of unfolding nets, thereby improving the efficiency of coverability determination. Furthermore, the reverse unfolding is applied to the formal verification of concurrent programs, and their data race detection is converted into the coverability determination of a specific state in 1-safe Petri nets. The experiment compares the efficiency between forward nfolding and reverse unfolding in the coverability determination of a Petri net. The results show that when the Petri net has more forward branches than backward branches, reverse unfolding is more efficient than forward unfolding. Finally, the key factors influencing the efficiency of reverse unfolding are analyzed.     

Heuristic search for scheduling flexible manufacturing systems using lower bound reachability matrix

For scheduling flexible manufacturing systems efficiently, we propose new heuristic functions for A^* algorithm that is based on the T-timed Petri net. In minimizing makespan, the proposed heuristic functions are usually more efficient than the previous functions in the required number of states and computation time. We prove that these heuristic functions are all admissible and one of them is more informed than that using resource cost reachability matrix. We also propose improved versions of these heuristic functions that find a first near-optimal solution faster. In addition, we modify the heuristic function of Yu, Reyes, Cang, and Lloyd (2003b) and propose an admissible version in all states. The experimental results using a random problem generator show that the proposed heuristic functions perform better as we expected.     

Web服务自动化测试技术

赋时Petri网为装配序列规划提供了有效的建模方法,但其在求解最优装配序列时受到组合复杂性的严重制约。零压缩二叉决策图(ZBDD)是处理大规模组合集合和0-1稀疏向量的一种有效符号技术,能够有效缓解组合爆炸问题。将赋时Petri网与ZBDD结合起来,给出了一种求解装配序列最优解的有效方法。首先通过转换算法将赋时Petri网转换为等价的普通Petri网,接下来给出普通Petri网可达状态及迁移引发函数的ZBDD表示方法,最后基于ZBDD给出最优装配序列求解算法。实例验证表明,该算法在求解过程中通过隐式符号操作实现了Petri网的可达状态搜索,有效缓解了计算过程中的组合复杂性。     

Heuristic search for scheduling flexible manufacturing systems using lower bound reachability matrix

For scheduling flexible manufacturing systems efficiently, we propose new heuristic functions for A^* algorithm that is based on the T-timed Petri net. In minimizing makespan, the proposed heuristic functions are usually more efficient than the previous functions in the required number of states and computation time. We prove that these heuristic functions are all admissible and one of them is more informed than that using resource cost reachability matrix. We also propose improved versions of these heuristic functions that find a first near-optimal solution faster. In addition, we modify the heuristic function of Yu, Reyes, Cang, and Lloyd (2003b) and propose an admissible version in all states. The experimental results using a random problem generator show that the proposed heuristic functions perform better as we expected.     

On the Regularity of Petri Net Languages

Petri nets are known to be useful for modeling concurrent systems. Once modeled by a Petri net, the behavior of a concurrent system can be characterized by the set of all executable transition sequences, which in turn can be viewed as a language over an alphabet of symbols corresponding to the transitions of the underlying Petri net. In this paper, we study the language issue of Petri nets from a computational complexity viewpoint. We analyze the complexity of theregularity problem(i.e., the problem of determining whether a given Petri net defines an irregular language or not) for a variety of classes of Petri nets, includingconflict-free,trap-circuit,normal,sinkless,extended trap-circuit,BPP, andgeneralPetri nets. (Extended trap-circuit Petri nets are trap-circuit Petri nets augmented with a specific type ofcircuits.) As it turns out, the complexities for these Petri net classes range from NL (nondeterministic logspace), PTIME (polynomial time), and NP (nondeterministic polynomial time), to EXPSPACE (exponential space). In the process of deriving the complexity results, we develop adecomposition approachwhich, we feel, is interesting in its own right, and might have other applications to the analysis of Petri nets as well. As a by-product, an NP upper bound of the reachability problem for the class of extended trap-circuit Petri nets (which properly contains that of trap-circuit (and hence, conflict-free) and BPP-nets, and is incomparable with that of normal and sinkless Petri nets) is derived.     

Preface: UNIGRA''03 - Uniform Approaches to Graphical Process Specification Techniques

This volume contains selected papers of the proceedings of the workshop on Uniform Approaches to Graphical Process Specification Techniques (UNIGRA'03). The workshop was held in Warsaw, Poland, on April 5 and 6, 2003, as a satellite event of the sixth European Joint Conference on Theory and Practice of Software (ETAPS 2003). The workshop continues the UNIGRA workshop in 2001 which has been a successful satellite event of ETAPS 2001.Workshop ObjectivesDue to the increasing amount of divergent formalisms, the main idea of the UNIGRA workshops is to bring together people working especially in the following three areas:

• Low Level and High-Level Petri Nets

• Graph Transformation and High-Level Replacement Systems

• Visual Modeling Techniques including UML

In each of these areas there is a large variety of different approaches, however, first attempts for uniform approaches have been made already. According to the main idea and in order to further stimulate the research in this important area, this volume presents some uniform approaches and further introduce unifying and comparative studies across the borders of the three and related areas.Workshop ProgramIn the first part, unifying approaches for low-level and high-level Petri nets are proposed:The contribution by Ehrig shows how the notions occurrence net and process can be generalized from low-level to high-level Petri nets, and studies the behavior and instantiations of this new view of processes for high-level nets.In his overview on new developments in the area of Petri net transformations for Software Engineering, Urbášek presents recent work on net model transformations and net class transformations. Both kinds of transformations are studied with regard to the preservation of system properties such as safety properties or liveness. The formalization of Petri net transformations is originally based on the theory of graph transformation.Padberg considers a case study (the call center of a phone company)which is modeled using Petri net modules for structuring the operational behavior of the system. The notion of Petri net modules was achieved by a transfer from the concepts of algebraic module specifications to the modeling of component-based systems by Petri nets.Desel, Juhás and Lorenz deal with the semantics of place/transition nets. The authors relate the process semantics based on partial orders (individual token semantics) to the collective token semantics by defining partial orders associated to process terms of place/transition nets.In the second part concerning graph transformation and high-level replacement systems, new aspects of component modeling and application of graph transformation techniques are discussed:In their contribution on components for algebra transformation systems, Ehrig and Orejas define a component transformation semantics in terms of the semantics of the specifications included in the components. The underlying formal basis of the instantiation of their generic component framework are algebra transformation systems and high-level replacement rules.An application of the formal unifying framework of distributed transformation units is presented by Kuske and Knirsch. The authors illustrate how different features of agent systems can be modeled by distributed graph transformation systems in a uniform way.Another application for graph rewriting, presented by Van Eetvelde and Janssens, is the modeling of refactoring operations for programs. The authors propose a hierarchical graph representation for programs to facilitate the study of refactoring operation effects at class level.The third part contains contributions focusing on unifying concepts for visual modeling techniques including UML:Minas describes a graphical specification tool for DIAGEN, a diagram editor generator based on hypergraph transformation. The specification tool simplifies the specification and generation of diagram editors. It uses an XML-based specification language and comes with a generic XML editor.In his contribution on dynamic aspects of visual modeling languages, Bottoni proposes an approach to the definition of the syntax and semantics of visual languages based on a notion of transition of production/consumption of resources. Abstract meta-models for this notion of transition are presented.An approach to the model-based verification and validation of properties of UML models is presented by Engels, Kïster, Heckel and Lohmann. The authors use graph transformation techniques as a meta-language for the translation and analysis of models.In model-driven architectures, the problem arises to deal with multiple models. Kent and Smith focus in their contribution on bidirectional mappings between models for software requirements and models for software design as basis for tools checking model traceability and consistency.Program CommitteeThe following program committee of UNIGRA'03 has given valuable scientific support:

• Hartmut Ehrig (TU Berlin, Germany) [chair]

• Roswitha Bardohl (TU Berlin, Germany) [co-chair]

• Luciano Baresi (University of Milano, Italy)

• Paolo Bottoni (University of Pisa, Italy)

• Claudia Ermel (TU Berlin, Germany)

• Reiko Heckel (University of Paderborn, Germany)

• Dirk Janssens (University of Antwerp, Belgium)

• Stuart Kent (University of Kent, Great Britain)

• Hans-Jörg Kreowski (University of Bremen, Germany)

• Fernando Orejas (University of Catalunya, Espania)

• Julia Padberg (University of Bremen, Germany)

• Grzegorz Rozenberg (University of Leiden, The Netherlands)

AcknowledgementThis workshop is supported by the European research training network SegraVis, and by the steering committee of the International Conference on Graph Transformation (ICGT).June 2003, Roswitha Bardohl and Hartmut Ehrig     

Covering sharing trees: a compact data structure for parameterized verification

The control state reachability problem is decidable for well-structured infinite-state systems like (Lossy) Petri Nets, Vector Addition Systems, and broadcast protocols. An abstract algorithm that solves the problem is the backward reachability algorithm of [1, 21 ]. The algorithm computes the closure of the predecessor operator with respect to a given upward-closed set of target states. When applied to this class of verification problems, symbolic model checkers based on constraints like [7, 26 ] suffer from the state explosion problem.In order to tackle this problem, in [13] we introduced a new data structure, called covering sharing trees, to represent in a compact way collections of infinite sets of system configurations. In this paper, we will study the theoretical complexity of the operations over covering sharing trees needed in symbolic model checking. We will also discuss several optimizations that can be used when dealing with Petri Nets. Among them, in [14] we introduced a new heuristic rule based on structural properties of Petri Nets that can be used to efficiently prune the search during symbolic backward exploration. The combination of these techniques allowed us to turn the abstract algorithm of [1, 21 ] into a practical method. We have evaluated the method on several finite-state and infinite-state examples taken from the literature [2, 18 , 20 , 30 ]. In this paper, we will compare the results we obtained in our experiments with those obtained using other finite and infinite-state verification tools.     

计算高级Petri网S-不变量的一种简单算法

在高级Petri网的性质分析中,S—不变量的方法是一个重要的方法,如何计算高级Petri网的S—不变量是一个重要课题。本文基于复合标志(Token)和标志流路的概念,给出了一个整系数线性方程系统,由该线性方程系统,可以得到高级Petri网的所有S—不变量,而不必将高级Petri网扩展为一般Petri网。     

Petri net modules in the transformation-based component framework

Component-based software engineering needs to be backed by thorough formal concepts and modeling techniques. This paper combines two concepts introduced independently by the two authors in previous papers. On one hand, the concept of Petri net modules introduced at IDPT 2002 in Padberg [J. Padberg, Petri net modules, Journal on Integrated Design and Process Technology 6 (4) (2002) 105–120], and on the other hand a generic component framework for system modeling introduced at FASE 2002 in Ehrig et al. [H. Ehrig, F. Orejas, B. Braatz, M. Klein, M. Piirainen, A generic component concept for system modeling, in: Proceedings of FASE ’02, Lecture Notes in Computer Science, vol. 2306, Springer, 2002]. First we develop a categorical formalization of the transformation based approach to components that is based on pushouts. This is the frame in which we show that Petri net modules can be considered as an instantiation of the generic component framework. This allows applying the transformation based semantics and compositionality result of the generic framework to Petri net modules. In addition to general Petri net modules we introduce Petri net modules preserving safety properties which can be considered as another instantiation of pushout based formalization of the generic framework.     

Can I find a partner? Undecidability of partner existence for open nets

We study open nets as Petri net models of web services, with a link to the practically relevant language WS-BPEL. For those nets, we investigate the problem of operability which we consider as fundamental as the successful notion of soundness for workflow nets, i.e., Petri net models of business processes and workflows. While we could give algorithmic solutions to the operability problem for subclasses of open nets in earlier work, this article shows that the problem is in general undecidable.