Generating a Petri net from a CSP specification: A semantics-based method

The paper is a partial synthesis of the work that a team within the Faculty of Managerial and Technological Engineering has in the field of modeling and simulation of systems with Petri nets. The paper deals with three issues. The first part is Modeling and simulation of manufacturing systems with timed Petri nets. The first part presents the way in which the performances of some manufacturing systems are evaluated using timed Petri nets. The first example is a manufacturing system specific to the textile industry. The system has three production lines. In this case, the modeling with timed Petri nets allows the analysis of the operation of the flow lines and highlights the bottleneck. Another modeled manufacturing system is specific to a series production, more precisely it refers to the manufacture of gas cookers within a company from Oradea. The model with Petri nets also describes the supply sequences of the stocks of parts and subassemblies. The next modeled system is an automated manufacturing system for the packaging of detergents. The complexity of the Detergent Packing System and the high level of automation, require the use of efficient modeling and simulation methods to verify the validity of the solutions adopted. In this chapter is present the model of a robotic welding cell. The second part of the paper, the transition from timed Petri nets to hierarchical colored Petri nets, shows how Petri nets were developed for a robotic cell for metallographic analysis. The third part is dedicated to modeling with colored Petri nets timed with complex colors of the flexible manufacturing cell A007 within the Department of Industrial Engineering.

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.

The specification and distributed control of discrete event robotic manufacturing systems using Petri nets are considered, and a methodology of decomposition and coordination is presented for hierarchical and distributed control. First, a task specification is defined as a Petri net model at the conceptual level, and then transformed to the detailed Petri net representation of the subtasks. Finally, the overall Petri net is decomposed and the constituent subnets are assigned to local Petri net based controllers. The controllers are coordinated by the coordinator so that the decomposed transitions fire at the same time. System coordination algorithm through communication between the coordinator and the controllers, is presented. By the proposed method, modeling, simulation and control of large and complex manufacturing systems can be performed consistently using Petri nets.

The research on modeling and simulation of complex biological systems is getting more important in Systems Biology. In this respect, we have developed Hybrid Function Petri net (HFPN) that was newly developed from existing Petri net because of their intuitive graphical representation and their capabilities for mathematical analyses. However, in the process of modeling metabolic, gene regulatory or signal transduction pathways with the architecture, we have realized three extensions of HFPN, (i) an entity should be extended to contain more than one value, (ii) an entity should be extended to handle other primitive types, e.g. boolean, string, (iii) an entity should be extended to handle more advanced type called object that consists of variables and methods, are necessary for modeling biological systems with Petri net based architecture. To deal with it, we define a new enhanced Petri net called hybrid functional Petri net with extension (HFPNe). To demonstrate the effectiveness of the enhancements, we model and simulate with HFPNe four biological processes that are diffcult to represent with the previous architecture HFPN.

The context of our work is the complex systems simulation. Complex systems modelling and simulation require to take into account the interactions between the different components. For instance, an airport ground traffic simulation requires to model the planes with the pilots, the control tower, the

Petri nets are a graph-based modelling formalism which has been widely used for the formal specification and analysis of concurrent systems. A common analysis technique is that of state space exploration (or reachability analysis). Here, every possible reachable state of the system is generated and desirable properties are evaluated for each state. This approach has the great advantage of conceptual simplicity, but the great disadvantage of being susceptible to state space explosion, where the number of states is simply too large for exhaustive exploration. Many reduction techniques have been suggested to ameliorate the problem of state space explosion. In the case of timed systems, the state space is infinite, unless analysis is restricted to a bounded time period. In this paper, we present a Petri net formalism based on the notion of relative time (as opposed to the traditional approach of dealing with absolute time). The goal is to derive a finite state space for timed systems which have repeating patterns of behaviour, even though time continues to advance indefinitely.

Specification and properties of a cache coherence protocol model.- GAMERU: A language for the analysis and design of human communication pragmatics within organizational systems.- Recent results on the complexity of problems related to Petri nets.- Algebraic structure of flows of a regular coloured net.- On equivalent execution semantics of concurrent systems.- Mathematical methods for calculating invariants in Petri nets.- On Petri nets with deterministic and exponentially distributed firing times.- An accurate performance model of CSMA/CD bus LAN.- Petri net models for the ?-calculus.- Fair processes.- Operational Petri net semantics for CCSP.- Infinitary languages of Petri nets and logical sentences.- A strong part of concurrency.- Concurrency and continuity.- Parallel systems specifications with coloured Petri nets and algebraic specifications.- Bibliography of Petri nets.

In the area of specification and modelling of concurrent systems, Petri nets have become a standard tool, and they still work behind the scenes in tools for graph transformation systems (cf. [1]). Moreover there is still potential for crossfertilization between the graph transformation and Petri net community. Even a better understanding of adhesive categories [2] and the related concepts of [3] seems possible in light of the proposed notion of weakly adhesive categories [4], which has emerged during work on the generalization of the co-reflective semantics of Petri nets to the realm of graph transformation and adhesive rewriting systems.KeywordsType ObjectGraph TransformationConcurrent SystemGraph GrammarGraph Transformation SystemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The use of Petri nets for modelling, analysing and simulating complex distributed production systems meets serious problems when the size of the model grows. Therefore, it would be very useful to decompose a Petri net based model into smaller models linked with one another. The aim of this paper is to suggest and discuss some possible definitions of Modular Petri nets. This is accomplished by introducing the concept of Petri subnet. Two possible definitions are proposed and the meaning and the usefulness with respect to both model definition and model executability for simulation are pointed out. All definitions are given for the basic model of Petri nets. The extension of modularity concepts to high level Petri nets is shown to be possible in the second part of the paper, where an application is illustrated. In particular an algorithm is given which allows automatic composition of subnets into a larger model

<u>1.1 The language CAP</u>While there are a couple of programming languages which allow the representation of parallelism /1,2,5/ there is a lack for languages which allow in an as well disciplined as general manner the description of concurrency.A well defined mathematical description method for concurrent processes is given by the Petri net model /3,7,9/. It fulfils the above requirements and in addition is widely used and extremely easy to understand.This concept is integrated into the language CAP in a very elegant way: Lables are used as places, where one has in mind that a labelled statement puts a token into its label(s) <u>after</u> it has been processed. On the other hand the processability of a statement is controlld by "On-conditions" on labels. Every statement is processed if and only if its "On-condition" has become true. At this time, in accordance with the firing-rule (="On-condition"), "tokens" are withdrawn from certain labels used within the "On-condition" and placed into the labels of the statement.In addition various parameters may be associated to transitions thus offering a description power similar to the Macro-E-Nets /8/. On the other hand there are a lot of language-constructs to support structured programming.<u>1.2 The analysis of CAP-programs at compile-time</u>Since a couple of years Petri nets are object of research. For some rather restricted subclasses of Petri nets sufficiant an necessary conditions for the topology of a net to be well-formed are known /3,4,7/. Under a well-formed net we understand a net <u>without dead-locks</u> being <u>safe</u> (no loss of information) and <u>residue-free</u> (independent from a certain history). Related to results by Herzog an Yoeli /4/ for a subclass of Petri nets we prove that there are six conditions for the topology of a net of the subclass of Petrinets which are used to describe the control-structure of CAP-programs so that the net is well-formed.By this we can decide at compile-time without simulation whether a CAP-program describes a life, safe and residue-free system (i. e. a useful one) or not. After having defined, what we mean ba a "Structured CAP-program" we will have the fine result that every structured CAP-program is well-formed.<u>1.3 The simulation of systems described in CAP</u>As CAP allows the description of systems down to a level of specification which is comparable with the bit-level of digital systems inclusive the detailled description of the real-time-behaviour, for the processing of CAP one needs a system similar to a simulator for digital circuits. On the other hand also very global descriptions on a high level of abstraction are possible.This implies that the run-time system for CAP must be extremely adaptive. We tried to solve this problem by a very flexible and powerful table driven and event oriented simulator with the event-mechanism being directly adopted from the Petri net concept of CAP.

Petri nets provide a well understood formal method for modeling concurrent systems, in all of their complexity. Petri nets, however, do not directly support the concepts of modularization, encapsulation, and information hiding that are essential to the successful abstraction of complexity provided by the OO methodology. The Petri net model of even a simple system can become overwhelmingly complex. The first goal of this paper was to survey a number of tools combining the OO technique with Petri nets, to pick one, and to use it in an implementation of an OO design. There was a great desire to utilize a tool having a graphical interface for the Petri net presentation. It was also highly desirable to utilize colored Petri nets. The design chosen was that of a bank ATM machine. The tool selected for use was SYROCO. This tool provides a means to define Cooperative objects (COO), which are translated into C++ classes. The COO language uses high level Petri nets to model the internal operation of objects, and provides a mechanism to connect together the Petri nets of distinct objects via the normal OO interface.

In this paper we focused our attention on a particular hybrid PN model called FOHPN, that is based on the fluidification of discrete PNs, and whose main feature is that the instantaneous firing speed of continuous transitions keeps constant during each macroperiod. In the first part of the paper we discuss in detail the advantages of fluidification, and provide a brief survey of the most important formalisms within the hybrid PN framework. Finally, we showed how FOHPNs can be efficiently used to model SC, and how interesting optimization problems can be solved via numerical simulation, by simply solving on-line a certain number of LPPs.

The aim of this work is the modeling and verification of concurrent systems subject to dynamic changes using extensions of Petri nets. We begin by introducing the notion of net rewriting system. In a net rewriting system, a system configuration is described as a Petri net and a change in configuration is described as a graph rewriting rule. We show that net rewriting systems are Turing powerful, that is, the basic decidable properties of Petri nets are lost and, thus, automatic verification in not possible for this class. A subclass of net rewriting systems are reconfigurable Petri nets. In a reconfigurable Petri net, a change in configuration amounts to the modification of the flow relations of the places in the domain of the involved rule according to this rule, independently of the context in which this rewriting applies. We show that reconfigurable Petri nets are formally equivalent to Petri nets. This equivalence ensures that all the fundamental properties of Petri nets are still decidable for reconfigurable Petri nets and this model is thus amenable to automatic verification tools. Therefore, the expressiveness of both models is the same, but, with reconfigurable Petri nets, we can easily and directly model systems that change their structure dynamically.

Petri nets have been widely used as a tool for modeling and analyzing concurrent and distributed system for many years but their applications have been limited to the earlier activities of software system development. To make Petri nets a full fledged software development methodology, systematic (eventually automatic) code generation techniques are needed. We present an approach to derive parallel program skeletons from Petri nets which establishes a link between Petri nets and OO parallel programming and forms a foundation for a Petri net based transformational software development methodology.

Petri nets have been extensively applied for specification, design, verification, performance evaluation, and simulation of discrete-event control systems. A real-time Petri net is a further improvement over the timed Petri net. The paper proposes to use a real-time Petri net to represent the stage programming of a programmable logic controller for a discrete-event control system. An illustrated example is used to explore the Petri net-based PLC stage programming methodology.