Markovian Testing Equivalence and Exponentially Timed Internal Actions

In the theory of testing for Markovian processes developed so far, exponentially timed internal actions are not admitted within processes. When present, these actions cannot be abstracted away, because their execution takes a nonzero amount of time and hence can be observed. On the other hand, they must be carefully taken into account, in order not to equate processes that are distinguishable from a timing viewpoint. In this paper, we recast the definition of Markovian testing equivalence in the framework of a Markovian process calculus including exponentially timed internal actions. Then, we show that the resulting behavioral equivalence is a congruence, has a sound and complete axiomatization, has a modal logic characterization, and can be decided in polynomial time

Testing Reactive Probabilistic Processes

We define a testing equivalence in the spirit of De Nicola and Hennessy for reactive probabilistic processes, i.e. for processes where the internal nondeterminism is due to random behaviour. We characterize the testing equivalence in terms of ready-traces. From the characterization it follows that the equivalence is insensitive to the exact moment in time in which an internal probabilistic choice occurs, which is inherent from the original testing equivalence of De Nicola and Hennessy. We also show decidability of the testing equivalence for finite systems for which the complete model may not be known

Characterising Testing Preorders for Finite Probabilistic Processes

In 1992 Wang & Larsen extended the may- and must preorders of De Nicola and Hennessy to processes featuring probabilistic as well as nondeterministic choice. They concluded with two problems that have remained open throughout the years, namely to find complete axiomatisations and alternative characterisations for these preorders. This paper solves both problems for finite processes with silent moves. It characterises the may preorder in terms of simulation, and the must preorder in terms of failure simulation. It also gives a characterisation of both preorders using a modal logic. Finally it axiomatises both preorders over a probabilistic version of CSP.Comment: 33 page

A uniform framework for modelling nondeterministic, probabilistic, stochastic, or mixed processes and their behavioral equivalences

Labeled transition systems are typically used as behavioral models of concurrent processes, and the labeled transitions define the a one-step state-to-state reachability relation. This model can be made generalized by modifying the transition relation to associate a state reachability distribution, rather than a single target state, with any pair of source state and transition label. The state reachability distribution becomes a function mapping each possible target state to a value that expresses the degree of one-step reachability of that state. Values are taken from a preordered set equipped with a minimum that denotes unreachability. By selecting suitable preordered sets, the resulting model, called ULTraS from Uniform Labeled Transition System, can be specialized to capture well-known models of fully nondeterministic processes (LTS), fully probabilistic processes (ADTMC), fully stochastic processes (ACTMC), and of nondeterministic and probabilistic (MDP) or nondeterministic and stochastic (CTMDP) processes. This uniform treatment of different behavioral models extends to behavioral equivalences. These can be defined on ULTraS by relying on appropriate measure functions that expresses the degree of reachability of a set of states when performing single-step or multi-step computations. It is shown that the specializations of bisimulation, trace, and testing equivalences for the different classes of ULTraS coincide with the behavioral equivalences defined in the literature over traditional models

On the Discriminating Power of Testing Equivalences for Reactive Probabilistic Systems: Results and Open Problems

International audienceTesting equivalences have been deeply investigated on fully nondeterministic processes, as well as on processes featuring probabilities and internal nondeterminism. This is not the case with reactive probabilistic processes, for which it is only known that the discriminating power of probabilistic bisimilarity is achieved when admitting a copying capability within tests. In this paper, we introduce for reactive probabilistic processes three testing equivalences without copying, which are respectively based on reactive probabilistic tests, fully nondeterministic tests, and nondeterministic and probabilistic tests. We show that the three testing equivalences are strictly finer than probabilistic failure-trace equivalence, and that the one based on nondeterministic and probabilistic tests is strictly finer than the other two, which are incomparable with each other. Moreover, we provide a number of facts that lead us to conjecture that (i) may testing and must testing coincide on reactive probabilistic processes and (ii) nondeterministic and probabilistic tests reach the same discriminating power as probabilistic bisimilarity

Equivalences on Phase Type Processes

In this thesis, we introduce Phase Type Processes (PTPs), a novel stochastic modeling approach that can express probabilistic and nondeterministic choices as well as random delays following phase type distributions, a generalization of exponential distributions. Action-labeled transitions are used to react on external stimuli and they are clearly separated from phase type transitions. The semantics of PTPs are defined in terms of path probabilities with respect to schedulers that resolve nondeterministic choices based on the timed process history. The main emphasis of this work is to analyze a variety of notions of equivalence for PTPs and classify them with respect to their distinguishing power. Amongst others, we define bisimulation, trace and testing equivalence as well as extensions of failure trace equivalence. Moreover, the contribution includes a discussion of parallel composition in the context of a partial memoryless property and the examination of a mapping from PTPs to the subclass of single phased processes in which all random delays are exponentially distributed

Modeling and verification of web service composition based interorganizational workflows

Interorganisationale Workflows sind Arbeitsabläufe, welche die Grenzen einer Organisation verlassen und einen Rahmen für Kooperationen der verschiedenen autonomen Organisationen zur Verfügung stellen. Ein wichtiger Punkt für den Entwurf solcher Workflows ist die Balance zwischen Offenheit und Abgrenzung, wobei erstere für Kooperationen und letztere die für den Schutz von Know-how benötigt wird. Workflow Sichten stellen ein effizientes Werkzeug für diesen Zweck zur Verfügung. Durch Offenlegung von bestimmten Teilen eines Prozesses, können Organisationen sowohl kooperieren als auch das Know-how schützen. Diese Dissertation präsentiert nun eine Methode für die korrekte Konstruktion von Workflow Sichten. Es wird angenommen, dass Organisationen Web Service orientierte Technologien zur Modellierung und Implementierung von interorganisationalen Workflows verwenden. Die Anwendung von Web Services bietet Organisationen viele Vorteile. Den eigentlichen Mehrwert von Web Services stellt aber die Kompositionsfähigkeit dar. Verfügbare Web Services können dadurch von anderen Choreographien und Orchestrationen (wieder-)verwendet werden. Die Notwendigkeit der Implementierung von Systemen von Null weg kann minimiert werden. Die zentralen Anforderungen sind einerseits eine Architektur mit adäquatem Potential, andererseits die Verifikation der Korrektheit. Diese Dissertation präsentiert nun eine Architektur zur Modellierung von Web Service Composition basierten interorganisationalen Workflows, genannt föderierte Choreographien, die verglichen mit anderen Architekturen verschiedene Vorteile anbieten. Darüber hinaus werden Algorithmen und Techniken zur Verifikation der strukturellen und temporalen Korrektheit vorgestellt. Strukturelle Korrektheit prüft, ob die Strukturen der beteiligten Prozesse zusammenpassen. Temporale Korrektheit überprüft, ob ein interorganisationaler Workflow, der aus mehreren Choreographien und Orchestrationen besteht hinsichtlich der lokalen und globalen Bedingungen fehlerfrei ist. Mit Hilfe dieser Techniken kann die strukturelle und temporale Konformität des Modells zur Designzeit überprüft werden. Falls das Modell nicht strukturell oder temporal konform ist, können nötige Änderungen durchgeführt werden, sodass die korrekte Ausführung zur Laufzeit garantiert werden kann. Die Überprüfung der Konformität zur Designzeit reduziert die Prozesskosten vor allem wegen den folgenden zwei Gründen: Erstens, die entdeckten Fehler zur Designzeit sind normalerweise billiger als jene, die zur Laufzeit entdeckt werden und zweitens, Fehlerbehandlungsmechanismen können verhindert werden, die wiederum Zusatzkosten verursachen. Zusätzlich zu der vorgestellten Architektur wird eine allgemeinere Architektur zusammen mit den passenden Konformitätsprüfungsalgorithmen präsentiert. Der Ansatz ist Platform- und sprachunabhängig und die Algorithmen sind verteilt.Interorganizational workflows are workflows that cross the boundaries of a single organization and provide a framework for cooperation of different autonomous organizations. An important issue when designing such workflows is the balance between the openness needed for cooperation and the privacy needed for protection of business know-how. Workflow views provide an efficient tool for this aim. By exposure of only selected parts of a process, organizations can both cooperate and protect their business logic. This dissertation presents a technique for a correct construction of workflow views. It is assumed that organizations and partners use web services and web service related technology to model and implement interorganizational workflows. Application of web services offers several advantages for organizations. The real surplus of web services is their capability of being composed to more complex systems. Available web services can be reused by other choreographies and orchestrations and the need for development of new systems from scratch can be minimized. The essential requirements are on the one hand an architecture with adequate capabilities and on the other hand, verification of correctness. This dissertation proposes an architecture for modeling web service composition based interorganizational workflows, called \emph{federated choreographies}, that provides several advantages compared to existing proposals. Moreover, algorithms and techniques for verification of structural and temporal correctness of interorganizational workflows are proposed. Structural conformance checks if the structures of the involved processes match. Temporal conformance checks if an interorganizational workflow composed of choreographies and orchestrations is temporally error-free with respect to local and global temporal constraints. The proposed algorithms can be applied for checking the structural and temporal conformance of the federated choreographies at design-time. If the model is not structurally or temporally conformant, necessary modifications can be done such that the correct execution of the flow at run-time can be guaranteed. The conformance checking at design time reduces the cost of process because of two reasons: first, errors detected at design time are normally cheaper than those detected at run time and second, exception handling mechanisms can be avoided which are, in turn, coupled with additional costs. In addition to the proposed architecture, a more general architecture together with the conformance checking algorithms and techniques for interorganizational workflows are presented. The presented approach is language and platform independent and algorithms work in a distributed manner