Analysis of Probabilistic Basic Parallel Processes

Basic Parallel Processes (BPPs) are a well-known subclass of Petri Nets. They are the simplest common model of concurrent programs that allows unbounded spawning of processes. In the probabilistic version of BPPs, every process generates other processes according to a probability distribution. We study the decidability and complexity of fundamental qualitative problems over probabilistic BPPs -- in particular reachability with probability 1 of different classes of target sets (e.g. upward-closed sets). Our results concern both the Markov-chain model, where processes are scheduled randomly, and the MDP model, where processes are picked by a scheduler.Comment: This is the technical report for a FoSSaCS'14 pape

Coloured Petri Nets - a Pragmatic Formal Method for Designing and Analysing Distributed Systems

The thesis consists of six individual papers, where the present paper contains the mandatory overview, while the remaining five papers are found separately from the overview. The five papers can roughly be divided into three areas of research, namely case studies, education, and extensions to the CPN method.The primary purpose of the PhD thesis is to study the pragmatics, practical aspects, and intuition of CP-nets viewed as a formal method for describing and reasoning about concurrent systems. The perspective of pragmatics is our leitmotif, but at the same time in the context of CP-nets it is a kind of hypothesis of this thesis. This overview paper summarises the research conducted as an investigation of the hypothesis in the three areas of case studies, education, and extensions.The provoking claim of pragmatics should not be underestimated. In the present overview of the thesis, the CPN method is compared with a representative selection of formal methods. The graphics and simplicity of semantics, yet generality and expressiveness of the language constructs, essentially makes CP-nets a viable and attractive alternative to other formal methods. Similar graphical formal methods, such as SDL and Statecharts, typically have significantly more complicated semantics, or are domain-specific languages.research conducted in this thesis, opens a new complex of problems. Firstly, to get wider acceptance of CP-nets in industry, it is important to identify fruitful areas for the effective introduction of the CPN method. Secondly, it would be useful to identify a few extensions to the CPN method inspired by specific domains for easier adaption in industry. Thirdly, which analysis methods do future systems make use of

ω-Inductive completion of monoidal categories and infinite petri net computations

There exists a KZ-doctrine on the 2-category of the locally small categories whose algebras are exactly the categories which admits all the colimits indexed by ω-chains. The paper presents a wide survey of this topic. In addition, we show that this chain cocompletion KZ-doctrine lifts smoothly to KZ-doctrines on (many variations of) the 2-categories of monoidal and symmetric monoidal categories, thus yielding a universal construction of colimits of ω-chains in those categories. Since the processes of Petri nets may be axiomatized in terms of symmetric monoidal categories this result provides a universal construction of the algebra of infinite processes of a Petri net

When are Stochastic Transition Systems Tameable?

A decade ago, Abdulla, Ben Henda and Mayr introduced the elegant concept of decisiveness for denumerable Markov chains [1]. Roughly speaking, decisiveness allows one to lift most good properties from finite Markov chains to denumerable ones, and therefore to adapt existing verification algorithms to infinite-state models. Decisive Markov chains however do not encompass stochastic real-time systems, and general stochastic transition systems (STSs for short) are needed. In this article, we provide a framework to perform both the qualitative and the quantitative analysis of STSs. First, we define various notions of decisiveness (inherited from [1]), notions of fairness and of attractors for STSs, and make explicit the relationships between them. Then, we define a notion of abstraction, together with natural concepts of soundness and completeness, and we give general transfer properties, which will be central to several verification algorithms on STSs. We further design a generic construction which will be useful for the analysis of {\omega}-regular properties, when a finite attractor exists, either in the system (if it is denumerable), or in a sound denumerable abstraction of the system. We next provide algorithms for qualitative model-checking, and generic approximation procedures for quantitative model-checking. Finally, we instantiate our framework with stochastic timed automata (STA), generalized semi-Markov processes (GSMPs) and stochastic time Petri nets (STPNs), three models combining dense-time and probabilities. This allows us to derive decidability and approximability results for the verification of these models. Some of these results were known from the literature, but our generic approach permits to view them in a unified framework, and to obtain them with less effort. We also derive interesting new approximability results for STA, GSMPs and STPNs.Comment: 77 page

A tool for model-checking Markov chains

Markov chains are widely used in the context of the performance and reliability modeling of various systems. Model checking of such chains with respect to a given (branching) temporal logic formula has been proposed for both discrete [34, 10] and continuous time settings [7, 12]. In this paper, we describe a prototype model checker for discrete and continuous-time Markov chains, the Erlangen-Twente Markov Chain Checker EÎMC2, where properties are expressed in appropriate extensions of CTL. We illustrate the general benefits of this approach and discuss the structure of the tool. Furthermore, we report on successful applications of the tool to some examples, highlighting lessons learned during the development and application of EÎMC2

Modelling Mutual Exclusion in a Process Algebra with Time-outs

I show that in a standard process algebra extended with time-outs one can correctly model mutual exclusion in such a way that starvation-freedom holds without assuming fairness or justness, even when one makes the problem more challenging by assuming memory accesses to be atomic. This can be achieved only when dropping the requirement of speed independence.Comment: arXiv admin note: text overlap with arXiv:2008.1335