Strictly synchronized sequential processes are characterized by a high degree of interdependence. The failure of a single such process can result in the deadlock of a large proportion of the entire system. We model a failure by removing the control token of a sequential process. A system design that limits such failures to the affected process can be very complicated. A method is presented whereby the crash of a sequential process does not affect the other processes.

Cycloids are particular Petri nets for modelling processes of actions and events, belonging to the fundaments of Petri's general systems theory. Defined by four parameters they provide an algebraic formalism to describe strongly synchronized sequential processes. To further investigate their structure, reduction systems of cycloids are defined in the style of rewriting systems and properties of irreducible cycloids are proved. In particular the synthesis of cycloid parameters from their Petri net structure is derived, leading to an efficient method for a decision procedure for cycloid isomorphism.

Cycloids are particular Petri nets for modelling processes of actions or events. They belong to the fundaments of Petri's general systems theory and have very different interpretations, ranging from Einstein's relativity theory and elementary information processing gates to the modelling of interacting sequential processes. This article contains previously unpublished proofs of cycloid properties using linear algebra.

Cycloids are particular Petri nets for modelling processes of actions and events, belonging to the funda-ments of Petri’s general systems theory. Defined by four parameters they provide an algebraic formalism to describe strongly synchronized sequential processes. To further investigate their structure, reduction systems of cycloids are studied. They allow for new synthesis approaches by deducing the parameters from the net structure.

The co-car anomaly appears in the study of circular traffic queues. An unfolding of the corresponding coloured net is proved to be isomorphic to a particular cycloid. Then the anomaly is reduced to a combinatorial property of path lengths in the cycloid. Methods of the cycloid algebra are used to derive iterations of cycloids. Different such iterations correspond to different models of traffic queues, but only those with observable co-traffic items show the anomaly.

Two sorts of circular traffic systems are defined and their minimal length of recurrent transition sequences is computed. The result is used for finding cycloids that have an isomorphic reachability graph. Cycloids are particular Petri nets for modelling processes of actions or events, belonging to the fundaments of Petri’s general systems theory. They have very different interpretations, ranging from Einstein’s relativity theory to elementary information processing gates. The cycloid representation of circular traffic systems allows to identify basic synchronisation mechanisms and leads to a structure theory of such systems.

Cycloids are particular Petri nets for modelling processes of actions or events. They belong to the fundaments of Petri’s general systems theory and have very different interpretations, ranging from Einstein’s relativity theory to elementary information processing gates. Despite their simple defini tions, their properties are still not completely understood. This contribution provides for the first time a formal definition together with new results concerning their structure. Cycloids are proved to be live and safe. It is shown that the minimal length of a cycle is the length of a local basic circuit, possibly decreased by an integer multiple of the number of semi-active transitions. These results allow to find the defining parameters of a cycloid from the static properties of the net system. Similar results are obtained for degenerate cycloids.

Cycloids are particular Petri nets for modelling processes of actions or events. They belong to the fundaments of Petri's general systems theory and have very different interpretations, ranging from Einstein's relativity theory to elementary information processing gates. Despite their simple definitions, their properties are still not completely understood. This contribution provides for the first time a formal definition together with new results concerning their structure. For instance, it is shown that the minimal length of a cycle is the length of a local basic circuit, possibly decreased by an integer multiple of the number of semi-active transitions.

From the Publisher: Formal methods for the specification and verification of hardware and software systems are becoming more and more important as systems increase in size and complexity. The aim of the book is to illustrate progress in formal methods, based on Petri net formalisms. It contains a collection of examples arising from different fields, such as flexible manufacturing, telecommunication and workflow management systems. The book covers the main phases in the life cycle of design and implementation of a system, i.e., specification, model checking techniques for verification, analysis of properties, code generation, and execution of models. These techniques and their tool support are discussed in detail including practical issues. Amongst others, fundamental concepts such as composition, abstraction, and reusability of models, model verification, and verification of properties are systematically introduced.

It is a pleasure to present a selection from the best papers of the 29th International Conference on Application and Theory of Petri Nets and Other Models of Concurrency (PETRI NETS 2008), held in Xi 'an, China, June 23-27, 2008.The Petri Net conference has already a long tradition and is well-known among the best theoreticians in computer science and also by people involved in practical applications.For more information about the Petri net conferences and related activities see: http://www.informatik.unihamburg.de/TGI/PetriNets/The Petri Net conference serves as the annual meeting place for researchers to exchange and to discuss the new results in the field of Petri Nets and other models of concurrency.Not only theoretical results are presented but also innovative applications.Novel tools, or substantial enhancements of existing tools for modeling, analysis or enactment of Petri Nets are presented as well.The conference always has a number of invited talks in which surveys on related fields are presented.The conference is always accompanied by workshops and tutorials.The 2008 conference had five invited speakers, two tutorials, four workshops and there was a tool exhibition.The conference received 75 submissions by authors from 21 different countries.The Program Committee accepted 23 papers, classified as: 14 theory papers, 5 application papers and 4 tool papers.The Petri Nets 2008 conference was organized by the Institute of Computing Theory and Technology at Xidian University, Xi'an, China.The Organizing Committee, chaired by Zhenhua Duan, did a very good job.This is the second time that the best papers presented at the conference are selected for a special issue of Fundamenta Informaticae.The authors of the selected papers were invited to submit substantially enhanced versions of their papers, which means that these papers differ significantly from the original conference papers.Each paper was reviewed according to the standards of the journal and if necessary revised by the authors.The seven selected papers in this special issue cover a variety of new results in theory as well as in applications.The paper "Synthesis of nets with step firing policies", introduces a way to control step semantics in order to restrict the concurrent behavior to improve modeling features.They also provide algorithms to synthesize a Petri net out of transition systems controlled by such a step firing policy.The paper "A net-based approach to Web services publication and replaceability" addresses the problem of interchangeability of services in arbitrary environments, based on an appropriate notion of behavioral equivalence.Further the paper introduces an ontology-based way of specifying services.In paper "Unfolding semantics of Petri nets based on token flows" two new unfolding semantics are presented that still

This contribution summarises the core results of the transdisciplinary ASKO project, part of the German DFG's programme Sozionik, which combines sociologists' and computer scientists' skills in order to create improved theories and models of artificial societies. Our research group has (a) formulated a social theory, which is able to explain fundamental mechanisms of self-organisation in both natural and artificial societies, (b) modelled this in a mathematical way using a visual formalism, and (c) developed a novel multi-agent system architecture which is conceptually coherent, recursively structured (hence non-eclectic) and based on our social theory. The article presents an outline of both a sociological middle-range theory of social self-organisation in educational institutions, its formal, Petri net based model, including a simulation of one of its main mechanisms, and the multi-agent system architecture SONAR. It describes how the theory was created by a re-analysis of some grand social theories, by grounding it empirically, and finally how the theory was evaluated by modelling its concepts and statements.

This correspondence introduces a deadlock-avoidance algorithm for a class of manufacturing systems with the following characteristics: 1) Production orders are allowed to have assembly operations (which give the nonsequential nature to the resource allocation system model) but not disassembly operations, 2) the use of system resources must be conservative (resources are neither created nor destroyed), and 3) actions related to the granting of resources are controllable. The proposed solution represents a sufficient condition for a given system state to be safe and is based on an adaptation of the well-known Banker's approach for deadlock avoidance. The time complexity of the proposed solution is proved to be polynomial with the size of the Place/Transition net model.

In this paper we give an overview of some formal models of concurrent systems, that are derived from the classical Petri net model. Since several of these models are introduced by Petri and his group within General Net Theory [4] they can also be called 'high-level Petri nets'. We discuss the motivation and usefulness of such extensions, as well as some of their disadvantages. While many of these models are only informally presented, we give a more formal definition of self-modifying nets together with a new presentation. On the other hand we do not consider such models that are combinations of Petri nets with other models, such as the program schemata of Roucairol f213 or evaluation nets of Noe [19~ .

The notion of linear place-invariants for coloured nets is extended to sums of non-linear functions. The extension applies to such places where all tokens are removed by the occurrence of an output transition. It is shown how this covers the case of variable assignments and invariants in traditional programs. The result helps in understanding the relation of place-invariants of coloured nets in comparison with traditional Floyd-invariants of programs. In the second part the property of token clearing is introduced to the occurrence rule, showing that the results of the first part are still valid. Such types of nets are important for the modelling of fault tolerant applications.