Showing papers on "Petri net published in 1991"

Modeling and verification of time dependent systems using time Petri nets

Abstract: A description and analysis of concurrent systems, such as communication systems, whose behavior is dependent on explicit values of time is presented. An enumerative method is proposed in order to exhaustively validate the behavior of P. Merlin's time Petri net model, (1974). This method allows formal verification of time-dependent systems. It is applied to the specification and verification of the alternating bit protocol as a simple illustrative example. >

Stubborn sets for reduced state space generation

Abstract: The “stubborn set” theory and method for generating reduced state spaces is presented. The theory takes advantage of concurrency, or more generally, of the lack of interaction between transitions, captured by the notion of stubborn sets. The basic method preserves all terminal states and the existence of nontermination. A more advanced version suited to the analysis of properties of reactive systems is developed. It is shown how the method can be used to detect violations of invariant properties. The method preserves the liveness (in Petri net sense) of transitions, and livelocks which cannot be exited. A modification of the method is given which preserves the language generated by the system. The theory is developed in an abstract variable/transition framework and adapted to elementary Petri nets, place/transition nets with infinite capacity of places, and coloured Petri nets.

Coloured Petri Nets: a high level language for system design and analysis

Abstract: This paper describes how Coloured Petri Nets (CP-nets) have been developed — from being a promising theoretical model to being a full-fledged language for the design, specification, simulation, validation and implementation of large software systems (and other systems in which human beings and/or computers communicate by means of some more or less formal rules).

High-level Petri Nets : Theory and Application

Abstract: The paper deals with conceptual, mathematical and practical aspects of developing a net theoretic system model. The model presented is based on common techniques of modelling static systems as structured sets of individuals (relational structures). These structures are 'dynamised' by allowing some relations between individuals to be changed by the processes of the modelled system.

A unified high-level Petri net formalism for time-critical systems

Abstract: The authors introduce a high-level Petri net formalism-environment/relationship (ER) nets-which can be used to specify control, function, and timing issues. In particular, they discuss how time can be modeled via ER nets by providing a suitable axiomatization. They use ER nets to define a time notation that is shown to generalize most time Petri-net-based formalisms which appeared in the literature. They discuss how ER nets can be used in a specification support environment for a time-critical system and, in particular, the kind of analysis supported. >

Branching processes of Petri nets

Abstract: 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.

Parallel and sequential mutual exclusions for petri net modeling of manufacturing systems with shared resources

Abstract: A theoretical basis for Petri net synthesis methods is provided that can be used to model systems with shared resources, and to make the resulting nets bounded, live, and reversible. Two resource-sharing concepts, parallel mutual exclusion (PME) and sequential mutual exclusion (SME), are formulated in the context of the Petri net theory. A PME models a resource shared by distinct independent processes, and an SME is a sequential composition of PMEs, modeling a resource shared by sequentially related processes. The conditions under which a net containing such structures remains bounded, live, and reversible are derived. >

Hierarchies in Coloured Petri Nets

Abstract: The paper shows how to extend Coloured Petri Nets with a hierarchy concept. The paper proposes five different hierarchy constructs, which allow the analyst to structure large CP-nets as a set of interrelated subnets (called pages). The paper discusses the properties of the proposed hierarchy constructs, and it illustrates them by means of two examples. The hierarchy constructs can be used for theoretical considerations, but their main use is to describe and analyse large real-world systems. All of the hierarchy constructs are supported by the editing and analysis facilities in the CPN Palette tool package (see [1–5]).

The Minimal Coverability Graph for Petri Nets

Abstract: We present the unique minimal coverability graph for Petri nets. When the reachability graph of a Petri net is infinite, the minimal coverability graph allows us to decide the same problems as the well-known Karp-Miller graph: the Finite Reachability Tree Problem, the Finite Reachability Set Problem, the Boundedness Problem, the Quasi-Liveness Problem and the Regularity Problem. The algorithm given for computing the minimal coverability graph is based on a new optimization of the Karp and Miller procedure.

On Time Petri Nets.

Abstract: In this chapter we study Time Petri nets: After the introduction of this kind of time-dependent Petri net, we will discuss variations of the rules defining the possible state changes. We then show how to reduce the state space of an arbitrary Time Petri net to a discrete one and use this to study the dynamic behavior of these time-dependent Petri nets under both qualitative and quantitative aspects.

Concurrent bisimulations in Petri nets

Abstract: After various attempts, an equivalence relation is defined for labelled Petri nets, on the base of the concurrency semantics of net theory. This relation, called Fully Concurrent bisimulation and abbreviated FC-bisimulation, preserves the level of concurrency of visible operations and, under some conditions, allows to enforce injective labelling on them. Refinements of a visible operation are also defined and we show that, under some conditions, they preserve FC-bisimulation.

A survey of behaviour and equivalence preserving refinements of Petri nets

Abstract: Results on refinements of places and transitions in Petri nets are surveyed. Such refinements may either transform a net to a refined net with the same behaviour, where behaviour often means safeness or liveness. Or they may transform semantically equivalent nets to refined nets which are semantically equivalent again. Here the semantics of a net is a description of the possible runs incorporating information on choices to a varying degree.

A Concept of Hierarchical Petri Nets with Building Blocks

Abstract: This paper introduces a formal concept of hierarchical Petri nets with building blocks The hierarchy concept allows to handle the refinement of places and transitions even if they are adjacent The building blocks are introduced as slightly restricted hierarchical Petri nets with hierarchically structured interfaces The main purpose of the concept is to facilitate the modeling of large real-world systems, rather than using them for theoretical considerations This will form the foundation of an editor-simulator-tool with a direct manipulation interface for this type of nets

Time, Petri nets, and robotics

Abstract: Based on the Petri net (PN) theory a particular class of condition/event nets called Omega , suitable for modeling repetitive workcell tasks, is defined. Nets in Omega are either deterministic or exhibit a restricted kind of conflict called choice among alternatives. It is shown how the repetitive behavior of such a net may be studied by decomposing this conflict into deterministic components associated with mutually exclusive alternatives. A unified description of the important temporal extensions of PN theory is presented, with emphasis on formal analysis. The PN notion of coverability is extended in the temporal sense and it is demonstrated that, for nets in Omega , the period of repetition (cycle time) can be directly computed from the durations associated with the individual operations, once the decomposition into components is performed. When the durations are specified in the form of minimum and maximum values, this period of repetition may be described by optimistic and pessimistic bounds. A typical assembly example adapted from work with a multirobot workcell testbed is also presented to illustrate two forms of temporal analysis. >

Advances in Petri Nets, 1990

Abstract: A survey of behaviour and equivalence preserving refinements of petri nets.- A distributed simulator for high order Petri nets.- Petri nets with uncertain markings.- Convex geometry and semiflows in P/T nets. A comparative study of algorithms for computation of minimal p-semiflows.- Improving the linearly based characterization of P/T nets.- Linear invariants in commutative high level nets.- Vicinity respecting net morphisms.- Regular stochastic petri nets.- Circuits, handles, bridges and nets.- On the analysis and synthesis of free choice systems.- Petri net models of a distributed election protocol on a unidirectional ring.- Hierarchies in coloured petri nets.- Coloured petri nets: A high level language for system design and analysis.- A simulation system architecture for graph models.- A state transformation preorder over a class of EN systems.- Composition of nets via a communication medium.- ?Trellis: A system for writing and browsing petri-net-based hypertext.- Stubborn sets for reduced state space generation.

From petri nets to linear logic

Abstract: Linear logic has recently been introduced by Girard as a logic of actions that seems well suited for concurrent computation. In this paper, we establish a systematic correspondence between Petri nets, linear logic theories, and linear categories. Such a correspondence sheds new light on the relationships between linear logic and concurrency, and on how both areas are related to category theory. Categories are here viewed as concurrent systems the objects of which are states, and the morphisms of which are transitions. This is an instance of the Lambek-Lawvere correspondence between logic and category theory that cannot be expressed within the more restricted framework of the Curry-Howard correspondence.

Circuits, handles, bridges and nets

Abstract: This paper introduces two new structural objects for the study of nets: handles and bridges. They are shown to provide sufficient, although not necessary, conditions of good behaviour for general ordinary nets, as well as a new characterisation of structural liveness and structural boundedness for the subclass of Free Choice nets. This characterisation is used to approach a modular synthesis theory of Free Choice nets through the synchronisation of State Machines. The task is fully performed for the restricted subclass of Strict Free Choice nets introduced here.

Ergodicity and throughput bounds of Petri nets with unique consistent firing count vector

Abstract: Ergodicity and throughput bound characterization are addressed for a subclass of timed and stochastic Petri nets, interleaving qualitative and quantitative theories. The nets considered represent an extension of the well-known subclass of marked graphs, defined as having a unique consistent firing count vector, independently of the stochastic interpretation of the net model. In particular, persistent and mono-T-semiflow net subclasses are considered. Upper and lower throughput bounds are computed using linear programming problems defined on the incidence matrix of the underlying net. The bounds proposed depend on the initial marking and the mean values of the delays but not on the probability distributions (thus including both the deterministic and the stochastic cases). From a different perspective, the considered subclasses of synchronized queuing networks; thus, the proposed bounds can be applied to these networks. >

Convex geometry and semiflows in P/T nets. A comparative study of algorithms for computation of minimal P-semiflows

Abstract: P-semiflows are non-negative left anullers of a net's flow matrix. The importance of these vectors lies in their usefulness for analyzing net properties. The concept of minimal p-semiflow is known in the context of Mathematical Programming under the name "extremal direction of a cone". This connection highlights a parallelism between properties found in the domains of P/T nets and Mathematical Programming. The algorithms known in the domain of P/T nets for computing elementary semi-flows are basically a new rediscovery, with technical improvements with respect to type of problems involved, of the basic Fourier-Motzkin method. One of the fundamental problems of these algorithms is their complexity. Various methods and rules for mitigating this problem are examined. As a result, this paper presents two improved algorithms which are more efficient and robust when handling "real-life" Nets.

Real-time systems performance in the presence of failures

Abstract: A unified methodology for modeling both soft and hard real-time systems is presented. Techniques that combine the effects of performance, reliability/availability, and deadline violation into a single model are used. An online transaction processing system is used as an example to illustrate the modeling techniques. Dynamic failures due to a transaction violating a hard deadline are taken into account by incorporating additional transitions in the Markov chain model of the failure-repair behavior. System performance in the various configurations is considered by using throughput and response-time distribution as reward rates. Since the Markov chains used in computing the distribution of response time are often very large and complex, a higher level interface based on a variation of stochastic Petri nets called stochastic reward nets is used. >

Compositional State Space Generation

Abstract: Compositional state space generation means the generation of a condensed version of the state space of a system in a compositional manner. The system is divided to parts. The state spaces of the parts are generated, condensed and composed to get a state space of the system. The method may be applied recursively; that is, the state spaces of the parts may have been generated compositionally. The generated condensed state space is in a certain sense equivalent with the ordinary state space, thus it can be used for the analysis of certain properties of the system.

Properties and performance bounds for closed free choice synchronized monoclass queueing networks

Abstract: It is shown that many monoclass queuing networks (QN) with synchronizations can naturally be modeled with a subclass of Petri nets (PN) called free-choice nets (FC), for which a wide gamut of qualitative behavioral and structural results have been derived. Some of these net theoretic results are used to characterize the ergodicity, boundedness, and liveness of closed free-choice synchronized QNs. Upper and lower throughput bounds are defined based on the mean value of the service times, without any assumption on the probability distributions (thus including both the deterministic and the stochastic cases). It is shown that monotonicity properties exist between the throughput bounds and the parameters of the model in terms of population and service times. Proposed are (theoretically polynomial and practically linear complexity) algorithms for the computation of these bounds, based on linear programming problems defined on the incidence matrix of the underlying FC net. Using classical laws from queuing theory, bounds are provided for mean queue lengths and response time. >