Target-oriented Petri Net Synthesis

We present two aspects of knitting technique, the structural properties (especially the P- and T-invariants), and the synchronized choice net (a new class of Petri net), that are of both theoretical importance and practical uses to the verification of structural correctness of a Petri net or to detect the structural problem of a Petri net. This work first proves that the ordinary Petri nets synthesized with knitting technique are structurally bounded, consistent, conservative and safe (when each home place holds one token) using the well-known linear algebra approach. It also provides a procedure for finding P- and T-invariants for Petri net synthesized using the knitting technique. We present examples for P-invariants and show that we can synthesize Petri nets more general than the "asymmetric-choice nets". The algorithm for finding P-invariants of ordinary Petri nets is extended to find the P-invariants for a general Petri net synthesized with knitting technique and the arc-ratio rules. We present a new class of Petri nets, called synchronized choice nets, which are the largest set of Petri nets that can be covered by both T-components and P-components. An algorithm is proposed to find its T-components and the P-components, respectively. The complexity of this algorithm is also presented. The theory of synchronized choice nets has the potential to simplify that for free choice nets.

Pre-synthesis of Petri nets based on prime cycles and distance paths

Petri nets have traditionally been motivated by their ability to express concurrency. Subclasses of Petri nets with concurrency but without choices or conflicts have been studied extensively. One of the best known - and comparatively restricted - such class are the marked graphs [4]. However, perhaps the largest class of (intuitively) choice-free nets are the persistent nets [7], a class of nets that is significantly larger than marked graphs. Some early results about persistent nets are Keller's theorem [6], which will be recalled in a later part of this paper, and the famous semilinearity result of Landweber and Robertson [7], which states that the set of reachable markings of a persistent net is semilinear. In this paper, we show that in bounded persistent nets, the smallest cycles of its reachability graph enjoy a uniqueness property.

In the area of Petri nets, many different developments have taken place within the last 30 years, in academia as well as in practice. For an adequate use in practice, a coherent and application oriented combination of various types and techniques for Petri nets is necessary. In order to attain a formal basis for different classes of Petri nets we introduce the concept of abstract Petri nets. The essential point of abstract Petri nets is to allow different kinds of net structures as well as the combination of various kinds of data types. This means that in abstract Petri nets the data type and the net structure part can be considered as abstract parameters which can be instantiated to different concrete net classes. We show that several net classes, like place/transition nets, elementary nets, S-graphs, algebraic high-level nets, and predicate/transitions nets are instantiations of abstract Petri nets. Moreover, we discuss coloured Petri nets in this context.KeywordsPredicate LogicForgetful FunctorUniform ApproachSpeci CationSignature Morphism

Team equivalences for finite-state machines with silent moves

<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.

The concept of siphons plays an important role in the analysis of Petri nets. In particular, criteria for liveness and reachability of some subclasses of Petri nets can be stated in terms of siphons. However, the computation of these structural components can be time consuming or even impossible. Recently, a variety of deadlock control policies that rely on partial siphon computation and enumeration have been developed. We propose a polynomial algorithm to find a set of elementary siphons in a class of Petri nets called systems of simple sequential processes with resources, S/sup 3/PR for short. Based on them, other siphons, called dependent ones, can be composed by simple set operations. Case studies show that the proposed algorithm is more computationally efficient than INA, integrated net analyzer, a widely used Petri net analysis tool.

Generic Petri net models of protocol mechanisms in communication systems

Petri nets are used as models of asynchronous concurrent systems. The underlying structure of a Petri net is a bipartite digraph. Many properties of Petri nets and the systems they model can be described in graph theoretic terms. These include the notions of deadlocks and traps. In this paper we consider these properties by restricting attention to some special classes of Petri nets including simple, complete, and free-choice Petri nets.

This study deals with deadlock problems in a system with uncontrollable and unobservable events, which is modeled with a subclass of Petri nets. We design monitors to enforce constraints for minimal siphons in a Petri net model. A key point of this paper is how to select the input and output arcs of a monitor when there exist uncontrollable and unobservable transitions. After the enforcement of constraints, an iterative algorithm is developed to obtain a controlled system with liveness. A sufficient and necessary condition is established to decide the existence of a monitor enforcing a constraint in a plant with uncontrollable and unobservable transitions.

Symmetric and Asymmetric Asynchronous Interaction

Petri nets have been widely used in the design of embedded controllers, namely in electronic hardware and computing platforms design, as well as within automation application areas. This paper presents updated characteristics of one class of Petri nets, named Input-Output Place-Transition Petri nets (IOPT nets), extended to support networked embedded controllers design and globally-asynchronous locally-synchronous (GALS) systems modeling, together with its associated metamodel and execution semantics. The proposed meta-model is compliant with the Petri Net Markup Language (PNML) metamodel, augmented with the descriptions for inputs and outputs, as well as for time domains and communication channels. The meta-model is described using UML class diagrams and has an equivalent Ecore meta-model that positioning IOPT nets within the Eclipse Modeling Framework (EMF).

With this contribution, we aim to draw a comprehensive classification of Petri nets with stopwatches w.r.t. expressiveness and decidability issues. This topic is too ambitious to be summarized in a single paper. That is why we present our results in two different parts. The scope of this first paper is to address the general results that apply for both dense-time and discrete-time semantics. We study the class of bounded Petri nets with stopwatches and reset arcs (rSwPNs), which is an extension of T-time Petri nets (TPNs) where time is associated with transitions. Stopwatches can be reset, stopped and started. We give the formal dense-time and discrete-time semantics of these models in terms of Transition Systems. We study the expressiveness of rSwPNs and its subclasses w.r.t. (weak) bisimilarity (behavioral semantics). The main results are following: 1) bounded rSw- PNs and 1-safe rSwPNs are equally expressive; 2) For all models, reset arcs add expressiveness. 3) The resulting partial classification of models is given by a set of relations explained in Fig. 7: in the forthcoming paper, we will complete these results by covering expressiveness and decidability issues when discrete-time nets are considered. For the sake of simplicity, our results are explained on a model such that the stopwatches behaviors are expressed using inhibitor arcs. Our conclusions can however be easily extended to the general class of Stopwatch Petri nets.

The work undertaken in this thesis is about the integration of two well-known methodologies: Petri net (PN) model Ii ng/analysis of industrial production processes and Artificial Intelligence (AI) optimisation search techniques. The objective of this integration is to demonstrate its potential in solving a difficult and widely studied problem, the scheduling of Flexible Manufacturing Systems (FIVIS). This work builds on existing results that clearly show the convenience of PNs as a modelling tool for FIVIS. It addresses the problem of the integration of PN and Al based search methods. Whilst this is recognised as a potentially important approach to the scheduling of FIVIS there is a lack of any clear evidence that practical systems might be built. This thesis presents a novel scheduling methodology that takes forward the current state of the art in the area by: Firstly presenting a novel modelling procedure based on a new class of PN (cb-NETS) and a language to define the essential features of basic FIVIS, demonstrating that the inclusion of high level FIVIS constraints is straight forward. Secondly, we demonstrate that PN analysis is useful in reducing search complexity and presents two main results: a novel heuristic function based on PN analysis that is more efficient than existing methods and a novel reachability scheme that avoids futile exploration of candidate schedules. Thirdly a novel scheduling algorithm that overcomes the efficiency drawbacks of previous algorithms is presented. This algorithm satisfactorily overcomes the complexity issue while achieving very promising results in terms of optimality. Finally, this thesis presents a novel hybrid scheduler that demonstrates the convenience of the use of PN as a representation paradigm to support hybridisation between traditional OR methods, Al systematic search and stochastic optimisation algorithms. Initial results show that the approach is promising.

This paper proposes an algorithm to generate the state space of Globally-Asynchronous-Locally-Synchronous (GALS) systems specified with a non-autonomous class of Petri nets. The Input-Output Place-Transition (IOPT) Petri net class is targeted to model automation and embedded systems. It extends the Place-Transition net class with non-autonomous features. To allow GALS systems specification with the IOPT Petri net class, Asynchronous-Channels are used to represent GALS components communication. As GALS systems tend to have large state spaces, a compilation strategy is used in order to improve generation performance. The presented algorithm is implemented in a C program through XSL transformations from the PNML file containing the IOPT net models of the GALS systems, which is then used to generate the intended state space and to identify a set of properties. After the state space analysis, the VHDL code of GALS components is automatically generated from the IOPT net specification, and implemented in FPGA based platforms.