A survey of the PEPA tools

This paper surveys the history and the current state of tool support for modelling with the PEPA stochastic process algebra and the PEPA nets modelling language. We discuss future directions for tool support for the PEPA family of languages.

Deterministic Petri net languages as business process specification language.

Today, a wide variety of techniques have been proposed to model the process aspects of business processes. The problem, however, is that many of these are focused on providing a clear graphical representation of the models and give almost no support for complex verification procedures. Alternatively, the use of Petri Nets as a business process modeling language has been repeatedly proposed. In complex business processes the use of Petri Nets has been criticized and the technique is believed to be unable to capture such processes in all aspects. Therefore, in this paper, we introduce the application of Petri Net language theory for business process specification. Petri Net languages are an extension to the Petri Net theory, and they provide a set of techniques to describe complex business processes more efficiently. More specifically, we advocate the application of deterministic Petri Net languages to model the control flow aspects of business processes. The balance between modeling power and analysis possibilities makes deterministic Petri Nets a highly efficient technique, used in a wide range of domains. The proof of their usability, as business process specification language, is given by providing suitable solutions to model the basic and more complex business process patterns [4]. Additionally, some points of particular interest are concisely discussed.Business; Business process modeling; Control; Model; Models; Patterns; Petri Net theory; Power; Process modeling; Processes; Representation; Theory; Verification;

The Reachability Problem for Petri Nets is Not Elementary

Petri nets, also known as vector addition systems, are a long established model of concurrency with extensive applications in modelling and analysis of hardware, software and database systems, as well as chemical, biological and business processes. The central algorithmic problem for Petri nets is reachability: whether from the given initial configuration there exists a sequence of valid execution steps that reaches the given final configuration. The complexity of the problem has remained unsettled since the 1960s, and it is one of the most prominent open questions in the theory of verification. Decidability was proved by Mayr in his seminal STOC 1981 work, and the currently best published upper bound is non-primitive recursive Ackermannian of Leroux and Schmitz from LICS 2019. We establish a non-elementary lower bound, i.e. that the reachability problem needs a tower of exponentials of time and space. Until this work, the best lower bound has been exponential space, due to Lipton in 1976. The new lower bound is a major breakthrough for several reasons. Firstly, it shows that the reachability problem is much harder than the coverability (i.e., state reachability) problem, which is also ubiquitous but has been known to be complete for exponential space since the late 1970s. Secondly, it implies that a plethora of problems from formal languages, logic, concurrent systems, process calculi and other areas, that are known to admit reductions from the Petri nets reachability problem, are also not elementary. Thirdly, it makes obsolete the currently best lower bounds for the reachability problems for two key extensions of Petri nets: with branching and with a pushdown stack.Comment: Final version of STOC'1

Hierarchical Communication Diagrams

Formal modelling languages range from strictly textual ones like process algebra scripts to visual modelling languages based on hierarchical graphs like coloured Petri nets. Approaches equipped with visual modelling capabilities make developing process easier and help users to cope with more complex systems. Alvis is a modelling language that combines possibilities of formal models verification with flexibility and simplicity of practical programming languages. The paper deals with hierarchical communication diagrams - the visual layer of the Alvis modelling language. It provides all necessary information to model system structure with Alvis, to manipulate a model hierarchy and to understand a model semantics. All considered concepts are discussed using illustrative examples

Formalisms for specifying Markovian population models

In this survey, we compare several languages for specifying Markovian population models such as queuing networks and chemical reaction networks. All these languages — matrix descriptions, stochastic Petri nets, stoichiometric equations, stochastic process algebras, and guarded command models — describe continuous-time Markov chains, but they differ according to important properties, such as compositionality, expressiveness and succinctness, executability, and ease of use. Moreover, they provide different support for checking the well-formedness of a model and for analyzing a model

Towards True Process Descriptions Interoperability

The article describes a part of our research in the area of (business) process modeling, analysis and execution. It describes the current state of process languages and standards. It concentrates on the process model interoperability and portability problems, caused because of huge number of process modeling standards, which often do not even target the same conceptual level of process modeling. It provides an idea how to bring together those standards, using process concepts mapping into Petri nets and incorporating the usage of process patterns. Transformation to strictly formal process languages has a potential to prove itself as a fair solution with the following advantages: the number of mappings among different process languages is reduced and the process model can be analyzed using proven Petri Net or general graph algorithms. Development of the approach is still in its early phase. Mapping rules to/from process patterns are neither strictly defined nor trivial, therefore, they will be the main focus of our future research

DecSerFlow: Towards a Truly Declarative Service Flow Language

The need for process support in the context of web services has triggered the development of many languages, systems, and standards. Industry has been developing software solutions and proposing standards such as BPEL, while researchers have been advocating the use of formal methods such as Petri nets and pi-calculus. The languages developed for service flows, i.e., process specification languages for web services, have adopted many concepts from classical workflow management systems. As a result, these languages are rather procedural and this does not fit well with the autonomous nature of services. Therefore, we propose DecSerFlow as a Declarative Service Flow Language. DecSerFlow can be used to specify, enact, and monitor service flows. The language is extendible (i.e., constructs can be added without changing the engine or semantical basis) and can be used to enforce or to check the conformance of service flows. Although the language has an appealing graphical representation, it is grounded in temporal logic

A regular viewpoint on processes and algebra

While different algebraic structures have been proposed for the treatment of concurrency, finding solutions for equations over these structures needs to be worked on further. This article is a survey of process algebra from a very narrow viewpoint, that of finite automata and regular languages. What have automata theorists learnt from process algebra about finite state concurrency? The title is stolen from [31]. There is a recent survey article [7] on finite state processes which deals extensively with rational expressions. The aim of the present article is different. How do standard notions such as Petri nets, Mazurkiewicz trace languages and Zielonka automata fare in the world of process algebra? This article has no original results, and the attempt is to raise questions rather than answer them