The complexity of Petri net transformations

Bibliography: pages 124-127.This study investigates the complexity of various reduction and synthesis Petri net transformations. Transformations that preserve liveness and boundedness are considered. Liveness and boundedness are possibly the two most important properties in the analysis of Petri nets. Unfortunately, although decidable, determining such properties is intractable in the general Petri net. The thesis shows that the complexity of these properties imposes limitations on the power of any reduction transformations to solve the problems of liveness and boundedness. Reduction transformations and synthesis transformations from the literature are analysed from an algorithmic point of view and their complexity established. Many problems regarding the applicability of the transformations are shown to be intractable. For reduction transformations this confirms the limitations of such transformations on the general Petri net. The thesis suggests that synthesis transformations may enjoy better success than reduction transformations, and because of problems establishing suitable goals, synthesis transformations are best suited to interactive environments. The complexity of complete reducibility, by reduction transformation, of certain classes of Petri nets, as proposed in the literature, is also investigated in this thesis. It is concluded that these transformations are tractable and that reduction transformation theory can provide insight into the analysis of liveness and boundedness problems, particularly in subclasses of Petri nets

Analyzing safety and fault tolerance using time Petri nets

The application of time Petri net modelling and analysis techniques to safety-critical real-time systems is explored and procedures described which allow analysis of safety, recoverability, and fault tolerance. These procedures can be used to help determine software requirements, to guide the use of fault detection and recovery procedures, to determine conditions which require immediate miti gating action to prevent accidents, etc. Thus it is possible to establish important properties duing the synthesis of the system and software design instead of using guesswork and costly a posteriori analysis

Verification and synthesis of asynchronous control circuits using petri net unfoldings

PhD ThesisDesign of asynchronous control circuits has traditionally been associated with application of formal methods. Event-based models, such as Petri nets, provide a compact and easy to understand way of specifying asynchronous behaviour. However, analysis of their behavioural properties is often hindered by the problem of exponential growth of reachable state space. This work proposes a new method for analysis of asynchronous circuit models based on Petri nets. The new approach is called PN-unfolding segment. It extends and improves existing Petri nets unfolding approaches. In addition, this thesis proposes a new analysis technique for Signal Transition Graphs along with an efficient verification technique which is also based on the Petri net unfolding. The former is called Full State Graph, the latter - STG-unfolding segment. The boolean logic synthesis is an integral part of the asynchronous circuit design process. In many cases, even if the verification of an asynchronous circuit specification has been performed successfully, it is impossible to obtain its implementation using existing methods because they are based on the reachability analysis. A new approach is proposed here for automated synthesis of speed-independent circuits based on the STG-unfolding segment constructed during the verification of the circuit's specification. Finally, this work presents experimental results showing the need for the new Petri net unfolding techniques and confirming the advantages of application of partial order approach to analysis, verification and synthesis of asynchronous circuits.The Research Committee, Newcastle University: Overseas Research Studentship Award

A methodology for analysis and control of discrete event dynamic systems

The rapid developments in computer technology have resulted in a widespread use of discrete event dynamic systems (DEDSs). This type of system is complex because it exhibits properties such as concurrency, conflict and non-determinism. It is therefore important to model and analyse such systems before implementation to ensure safe, deadlock free and optimal operation. This thesis investigates current modelling techniques and describes Petri net theory in more detail. It reviews top down, bottom up and hybrid Petri net synthesis techniques that are used to model large systems and introduces on object oriented methodology to enable modelling of larger and more complex systems. Designs obtained by this methodology are modular, easy to understand and allow re-use of designs. Control is the next logical step in the design process. This thesis reviews recent developments in control DEDSs and investigates the use of Petri nets in the design of supervisory controllers. The scheduling of exclusive use of resources is investigated and an efficient Petri net based scheduling algorithm is designed and a re-configurable controller is proposed. To enable the analysis and control of large and complex DEDSs, an object oriented C++ software tool kit was developed and used to implement a Petri net analysis tool, Petri net scheduling and control algorithms. Finally, the methodology was applied to two industrial DEDSs: a prototype can sorting machine developed by Eurotherm Controls Ltd., and a semiconductor testing plant belonging to SGS Thomson Microelectronics Ltd

Scheduling and discrete event control of flexible manufacturing systems based on Petri nets

A flexible manufacturing system (FMS) is a computerized production system that can simultaneously manufacture multiple types of products using various resources such as robots and multi-purpose machines. The central problems associated with design of flexible manufacturing systems are related to process planning, scheduling, coordination control, and monitoring. Many methods exist for scheduling and control of flexible manufacturing systems, although very few methods have addressed the complexity of whole FMS operations. This thesis presents a Petri net based method for deadlock-free scheduling and discrete event control of flexible manufacturing systems. A significant advantage of Petri net based methods is their powerful modeling capability. Petri nets can explicitly and concisely model the concurrent and asynchronous activities, multi-layer resource sharing, routing flexibility, limited buffers and precedence constraints in FMSs. Petri nets can also provide an explicit way for considering deadlock situations in FMSs, and thus facilitate significantly the design of a deadlock-free scheduling and control system. The contributions of this work are multifold. First, it develops a methodology for discrete event controller synthesis for flexible manufacturing systems in a timed Petri net framework. The resulting Petri nets have the desired qualitative properties of liveness, boundedness (safeness), and reversibility, which imply freedom from deadlock, no capacity overflow, and cyclic behavior, respectively. This precludes the costly mathematical analysis for these properties and reduces on-line computation overhead to avoid deadlocks. The performance and sensitivity of resulting Petri nets, thus corresponding control systems, are evaluated. Second, it introduces a hybrid heuristic search algorithm based on Petri nets for deadlock-free scheduling of flexible manufacturing systems. The issues such as deadlock, routing flexibility, multiple lot size, limited buffer size and material handling (loading/unloading) are explored. Third, it proposes a way to employ fuzzy dispatching rules in a Petri net framework for multi-criterion scheduling. Finally, it shows the effectiveness of the developed methods through several manufacturing system examples compared with benchmark dispatching rules, integer programming and Lagrangian relaxation approaches

PETRI NET BASED MODELING OF PARALLEL PROGRAMS EXECUTING ON DISTRIBUTED MEMORY MULTIPROCESSOR SYSTEMS

The development of parallel programs following the paradigm of communicating sequen- tial processes to be executed on distributed memory multiprocessor systems is addressed. The key issue in programming parallel machines today is to provide computerized tools supporting the development of efficient parallel software, i.e. software effectively har- nessing the power of parallel processing systems. The critical situations where a parallel programmer needs help is in expressing a parallel algorithm in a programming language, in getting a parallel program to work and in tuning it to get optimum performance (for example speedup). . We show that the Petri net formalism is higly suitable as a performance modeling technique for asynchronous parallel systems, by introducing a model taking care of the parallel program, parallel architecture and mapping influences on overall system perfor- mance. PRM -net (Program-Resource- Mapping) models comprise a Petri net model of the multiple flows of control in a parallel program, a Petri net model of the parallel hardware and the process-to-processor mapping information into a single integrated performance model. Automated analysis of PRM-net models addresses correctness and performance of parallel programs mapped to parallel hardware. Questions upon the correctness of parallel programs can be answered by investigating behavioural properties of Petri net programs like liveness, reachability, boundedness, mutualy exclusiveness etc. Peformance of parallel programs is usefully considered only in concern with a dedicated target hard- ware. For this reason it is essential to integrate multiprocessor hardware characteristics into the specification of a parallel program. The integration is done by assigning the concurrent processes to physical processing devices and communication patterns among parallel processes to communication media connecting processing elements yielding an in- tegrated, Petri net based performance model. Evaluation of the integrated model applies simulation and markovian analysis to derive expressions characterising the peformance of the program being developed. Synthesis and decomposition rules for hierarchical models naturally give raise to use PRM-net models for graphical, performance oriented parallel programming, support- ing top-down (stepwise refinement) as well as bottom-up development approaches. The graphical representation of Petri net programs visualizes phenomena like parallelism, syn- chronisation, communication, sequential and alternative execution. Modularity of pro- gram blocks aids reusability, prototyping is promoted by automated code generation on the basis of high level program specifications

Formulation of Cell Petri Nets

Based on the Petri net definitions and theorems already formalized in the Mizar article [13], in this article we were able to formalize the definition of cell Petri nets. It is based on [12]. Colored Petri net has already been defined in [11]. In addition, the conditions of the firing rule and the colored set to this definition, that defines the cell Petri nets are further extended to CPNT.i further. The synthesis of two Petri nets was introduced in [11] and in this work the definition is extended to produce the synthesis of a family of colored Petri nets. Specifically, the extension to a CPNT family is performed by specifying how to link the outbound transitions of each colored Petri net to the place elements of other nets to form a neighborhood relationship. Finally, the activation of colored Petri nets was formalized.Jitsukawa Mitsuru - Shinshu University Nagano, JapanKawamoto Pauline N. - Shinshu University Nagano, JapanShidama Yasunari - Shinshu University Nagano, JapanGrzegorz Bancerek. König’s theorem. Formalized Mathematics, 1(3):589-593, 1990.Grzegorz Bancerek. Free term algebras. Formalized Mathematics, 20(3):239-256, 2012. doi:10.2478/v10037-012-0029-6.Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Czesław Bylinski. The modification of a function by a function and the iteration of the composition of a function. Formalized Mathematics, 1(3):521-527, 1990.Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.Mitsuru Jitsukawa, Pauline N. Kawamoto, Yasunari Shidama, and Yatsuka Nakamura. Cell Petri net concepts. Formalized Mathematics, 17(1):37-42, 2009. doi:10.2478/v10037-009-0004-z.Pauline N. Kawamoto and Yatsuka Nakamura. On Cell Petri Nets. Journal of Applied Functional Analysis, 1996.Pauline N. Kawamoto, Yasushi Fuwa, and Yatsuka Nakamura. Basic Petri net concepts. Formalized Mathematics, 3(2):183-187, 1992.Krzysztof Retel. Properties of first and second order cutting of binary relations. Formalized Mathematics, 13(3):361-365, 2005.Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1): 115-122, 1990.Andrzej Trybulec. Many sorted sets. Formalized Mathematics, 4(1):15-22, 1993.Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990

Analysis of Petri Nets and Transition Systems

This paper describes a stand-alone, no-frills tool supporting the analysis of (labelled) place/transition Petri nets and the synthesis of labelled transition systems into Petri nets. It is implemented as a collection of independent, dedicated algorithms which have been designed to operate modularly, portably, extensibly, and efficiently.Comment: In Proceedings ICE 2015, arXiv:1508.0459

Pragmatic approach to the development of robust real-time protocols

This research is concerned with the development of distributed real-time systems, in which software is used for the control of concurrent physical processes. These distributed control systems are required to periodically coordinate the operation of several autonomous physical processes, with the property of an atomic action. The implementation of this coordination must be fault-tolerant if the integrity of the system is to be maintained in the presence of processor or communication failures. Commit protocols have been widely used to provide this type of atomicity and ensure consistency in distributed computer systems. The objective of this research is the development of a class of robust commit protocols, applicable to the coordination of distributed real-time control systems. Extended forms of the standard two phase commit protocol, that provides fault-tolerant and real-time behaviour, were developed. Petri nets are used for the design of the distributed controllers, and to embed the commit protocol models within these controller designs. This composition of controller and protocol model allows the analysis of the complete system in a unified manner. A common problem for Petri net based techniques is that of state space explosion, a modular approach to both the design and analysis would help cope with this problem. Although extensions to Petri nets that allow module construction exist, generally the modularisation is restricted to the specification, and analysis must be performed on the (flat) detailed net. The Petri net designs for the type of distributed systems considered in this research are both large and complex. The top down, bottom up and hybrid synthesis techniques that are used to model large systems in Petri nets are considered. A hybrid approach to Petri net design for a restricted class of communicating processes is developed. Designs produced using this hybrid approach are modular and allow re-use of verified modules. In order to use this form of modular analysis, it is necessary to project an equivalent but reduced behaviour on the modules used. These projections conceal events local to modules that are not essential for the purpose of analysis. To generate the external behaviour, each firing sequence of the subnet is replaced by an atomic transition internal to the module, and the firing of these transitions transforms the input and output markings of the module. Thus local events are concealed through the projection of the external behaviour of modules. This hybrid design approach preserves properties of interest, such as boundedness and liveness, while the systematic concealment of local events allows the management of state space. The approach presented in this research is particularly suited to distributed systems, as the underlying communication model is used as the basis for the interconnection of modules in the design procedure. This hybrid approach is applied to Petri net based design and analysis of distributed controllers for two industrial applications that incorporate the robust, real-time commit protocols developed. Temporal Petri nets, which combine Petri nets and temporal logic, are used to capture and verify causal and temporal aspects of the designs in a unified manner

Mining structured Petri nets for the visualization of process behavior

Visualization is essential for understanding the models obtained by process mining. Clear and efficient visual representations make the embedded information more accessible and analyzable. This work presents a novel approach for generating process models with structural properties that induce visually friendly layouts. Rather than generating a single model that captures all behaviors, a set of Petri net models is delivered, each one covering a subset of traces of the log. The models are mined by extracting slices of labelled transition systems with specific properties from the complete state space produced by the process logs. In most cases, few Petri nets are sufficient to cover a significant part of the behavior produced by the log.Peer ReviewedPostprint (author's final draft