Results 1  10
of
89
Complexity Results for 1safe Nets
, 1993
"... We study the complexity of several standard problems for 1safe Petri nets and some of its subclasses. We prove that reachability, liveness, and deadlock are all PSPACEcomplete for 1safe nets. We also prove that deadlock is NPcomplete for freechoice nets and for 1safe freechoice nets. Finally, ..."
Abstract

Cited by 44 (7 self)
 Add to MetaCart
We study the complexity of several standard problems for 1safe Petri nets and some of its subclasses. We prove that reachability, liveness, and deadlock are all PSPACEcomplete for 1safe nets. We also prove that deadlock is NPcomplete for freechoice nets and for 1safe freechoice nets. Finally, we prove that for arbitrary Petri nets, deadlock is equivalent to reachability and liveness. This paper is to be presented at FST&TCS 13, Foundations of Software Technology & Theoretical Computer Science, to be held 1517 December 1993, in Bombay, India. A version of the paper with most proofs omitted is to appear in the proceedings. 1 Introduction Petri nets are one of the oldest and most studied formalisms for the investigation of concurrency [33]. Shortly after the birth of complexity theory, Jones, Landweber, and Lien studied in their classical paper [24] the complexity of several fundamental problems for Place/Transition nets (called in [24] just Petri nets). Some years later, Howell,...
ZeroSafe Nets: Comparing the Collective and Individual Token Approaches
"... The main feature of zerosafe nets is a primitive notion of transition synchronization. To this aim, besides ordinary places, called stable places, zerosafe nets are equipped with zero places, which in an observable marking cannot contain any token. This yields the notion of transaction: a basic ..."
Abstract

Cited by 40 (20 self)
 Add to MetaCart
The main feature of zerosafe nets is a primitive notion of transition synchronization. To this aim, besides ordinary places, called stable places, zerosafe nets are equipped with zero places, which in an observable marking cannot contain any token. This yields the notion of transaction: a basic atomic computation, which may use zero tokens as triggers, but defines an evolution between observable markings only. The abstract counterpart of a generic zerosafe net B consists of an ordinary P/T net whose places are the stable places of B, and whose transitions represent the transactions of B. The two nets offer both the refined and the abstract model of the same system, where the former can be much smaller than the latter, because of the transition synchronization mechanism. Depending on the chosen approach  collective vs individual token philosophy  two notions of transaction may be defined, each leading to different operational and abstract models. Their comparison is fully dis...
The PEP Tool
, 1997
"... The PEP tool is a Programming Environment based on Petri Nets. Comprehensive modelling, compilation, simulation and verification components are embedded in a userfriendly graphical interface. The basic idea is that the modelling component allows the user to design parallel systems by parallel finit ..."
Abstract

Cited by 35 (2 self)
 Add to MetaCart
The PEP tool is a Programming Environment based on Petri Nets. Comprehensive modelling, compilation, simulation and verification components are embedded in a userfriendly graphical interface. The basic idea is that the modelling component allows the user to design parallel systems by parallel finite automata, parallel programs, process algebra terms, highlevel or lowlevel Petri nets, and that the PEP system then automatically generates Petri nets from such models in order to use Petri net theory for simulation and verification purposes. This paper describes the typical usage of the PEP tool by considering the design of the wellknown `alternatingbit' protocol. Among others, the usefulness of new concepts for the handling of hierarchies and synchronous communication is explained. PEP has been implemented on Solaris 2.x, SunOS 4.1.x and Linux. Ftpable versions are available via http://www.informatik.unihildesheim.de/¸pep. Keywords: `Alternating bit' protocol, B(PN) 2 , Hierarc...
Action Structures
, 1992
"... Action structures are proposed as a variety of algebra to underlie concrete models of concurrency and interaction. An action structure is equipped with composition and product of actions, together with two other ingredients: an indexed family of abstractors to allow parametrisation of actions, a ..."
Abstract

Cited by 34 (1 self)
 Add to MetaCart
Action structures are proposed as a variety of algebra to underlie concrete models of concurrency and interaction. An action structure is equipped with composition and product of actions, together with two other ingredients: an indexed family of abstractors to allow parametrisation of actions, and a reaction relation to represent activity. The eight axioms of an action structure make it an enriched strict monoidal category; however, the work is presented algebraically rather than in category theory. The notion of action structure is developed mathematically, and examples are studied ranging from the evaluation of expressions to the statics and dynamics of Petri nets. For algebraic process calculi in particular, it is shown how they may be defined by a uniform superposition of process structure upon an action structure specific to each calculus. This allows a common treatment of bisimulation congruence. The theory of action structures emphasizes the notion of effect; that ...
A Comparison of Performance Evaluation Process Algebra and Generalized Stochastic Petri Nets
 In Proc. 6th International Workshop on Petri Nets and Performance Models
, 1995
"... Generalized Stochastic Petri Nets (GSPN)and Performance Evaluation Process Algebra (PEPA) can both be used to study qualitative and quantitative behaviour of systems in a single environment. This paper presents a comparison of the two formalisms in terms of the facilities that they provide to the mo ..."
Abstract

Cited by 28 (7 self)
 Add to MetaCart
Generalized Stochastic Petri Nets (GSPN)and Performance Evaluation Process Algebra (PEPA) can both be used to study qualitative and quantitative behaviour of systems in a single environment. This paper presents a comparison of the two formalisms in terms of the facilities that they provide to the modeller, considering both the definition and the analysis of the performance model. Our goal is to provide a better understanding of both formalisms, and to prepare a fertile ground for exchanging ideas and techniques between the two. To illustrate similarities and differences, we make the different issues more concrete by means of an example modelling resource contention. 1 Introduction In this paper we present a comparison of two formalisms which may be used to develop performance models as continuous time Markov chains (CTMC). Generalized stochastic Petri nets (GSPN) is a wellestablished high level modelling paradigm which has been widely applied in performance analysis. In contrast, Per...
A Comprehensive Study of the Complexity of Multiparty Interaction
 Journal of the ACM
, 1996
"... A multiparty interaction is a set of I/O actions executed jointly by a number of processes, each of which must be ready to execute its own action for any of the actions in the set to occur. An attempt to participate in an interaction delays a process until all other participants are available. Altho ..."
Abstract

Cited by 26 (8 self)
 Add to MetaCart
A multiparty interaction is a set of I/O actions executed jointly by a number of processes, each of which must be ready to execute its own action for any of the actions in the set to occur. An attempt to participate in an interaction delays a process until all other participants are available. Although a relatively new concept, the multiparty interaction has found its way into a number of distributed programming languages and algebraic models of concurrency. In this paper, we present a taxonomy of languages for multiparty interaction that covers all proposals of which we are aware. Based on this taxonomy, we then present a comprehensive analysis of the computational complexity of the multiparty interaction scheduling problem, the problem of scheduling multiparty interactions in a given execution environment. 1 Introduction A multiparty interaction is a set of I/O actions executed jointly by a number of processes, each of which must be ready to execute its own action for any of the act...
PEP  More than a Petri Net Tool
, 1996
"... The PEP system (Programming Environment based on Petri Nets) supports the most important tasks of a good net tool, including HL and LL net editing and comfortable simulation facilities. In addition, these features are embedded in sophisticated programming and verification components. The programming ..."
Abstract

Cited by 24 (2 self)
 Add to MetaCart
The PEP system (Programming Environment based on Petri Nets) supports the most important tasks of a good net tool, including HL and LL net editing and comfortable simulation facilities. In addition, these features are embedded in sophisticated programming and verification components. The programming component allows the user to design concurrent algorithms in an easytouse imperative language, and the PEP system then generates Petri nets from such programs. The PEP tool's comprehensive verification components allow a large range of properties of parallel systems to be checked efficiently on either programs or their corresponding nets. This includes userdefined properties specified by temporal logic formulae as well as specific properties for which dedicated algorithms are available. PEP has been implemented on Solaris 2.4, SunOS 4.1.3 and Linux. Ftpable versions are available.
A Class of Composable High Level Petri Nets
, 1995
"... In this paper a highlevel Petri net model called Mnets (for multilabeled nets) is developed. A distinctive feature of this model is that it allows not only vertical unfolding, as do most other highlevel net models, but also horizontal composition  in particular, synchronisation  in a manner sim ..."
Abstract

Cited by 23 (11 self)
 Add to MetaCart
In this paper a highlevel Petri net model called Mnets (for multilabeled nets) is developed. A distinctive feature of this model is that it allows not only vertical unfolding, as do most other highlevel net models, but also horizontal composition  in particular, synchronisation  in a manner similar to process algebras such as CCS. This turns the set of Mnets into a domain whose composition operations satisfy various algebraic properties. The operations are shown to be consistent with unfolding in the sense that the unfolding of a composite highlevel net is the composition of the unfoldings of its components. A companion paper shows how this algebra can be used to define the semantics of a concurrent programming language compositionally. 1 Introduction and Motivation In traditional highlevel Petri net models, as described for instance in [1, 10, 11, 16, 17, 20, 21], there are place/transition annotations which determine the transition rule of the model. Such annotations also dr...
An Event Structure Semantics for General Petri Nets
 Theoretical Computer Science
, 1993
"... In this paper we address the following question: What type of event structures are suitable for representing the behaviour of general Petri nets? As a partial answer to this question we define a new class of event structures called local event structures and identify a subclass called ULevent stru ..."
Abstract

Cited by 21 (1 self)
 Add to MetaCart
In this paper we address the following question: What type of event structures are suitable for representing the behaviour of general Petri nets? As a partial answer to this question we define a new class of event structures called local event structures and identify a subclass called ULevent structures. We propose that ULevent structures are appropriate for capturing the behaviour of general Petri nets. Our answer is a partial one in that in the proposed event structure semantics, autoconcurrency is filtered out from the behaviour of Petri nets. It turns out that this limited event structure semantics for Petri nets is nevertheless a nontrivial and conservative extension of the (prime) event structure semantics of 1safe Petri nets provided in [NPW]. We also show that the strong relationship between prime event structures and 1safe Petri nets established in a categorical framework in [W3] can be extended to the present setting, provided we restrict our attention to the subclass ...