Diego Latella

Towards a Formal Operational Semantics of UML Statechart Diagrams

Statechart Diagrams are a notation for describing behaviours in the framework of UML, the Unified Modeling Language of object-oriented systems. UML is a semi-formal language, with a precisely defined syntax and static semantics but with an only informally specified dynamic semantics. UML Statechart Diagrams differ from classical statecharts, as defined by Harel, for which formalizations and results are available in the literature. This paper sets the basis for the development of a formal semantics for UML Statechart Diagrams based on Kripke structures. This forms the first step towards model checking of UML Statechart Diagrams. We follow the approach proposed by Mikk and others: we first map Statechart Diagrams to the intermediate format of extended hierarchical automata and then we define an operational semantics for these automata. We prove a number of properties of such semantics which reflect the design choices of UML Statechart Diagrams.

Model checking UML Statechart diagrams using JACK

Statechart diagrams provide a graphical notation for describing dynamic aspects of system behaviour within the Unified Modelling Language (UML). In this paper, we present a branching-time model-checking approach to the automatic verification of the formal correctness of UML Statechart diagram specifications. We use a formal operational semantics for building a labelled transition system (automaton) which is then used as a model to be checked against correctness requirements expressed in Action-Based Temporal Logic (ACTL). Our reference verification environment is JACK, where automata are represented in a standard format, which facilitates the use of different tools for automatic verification.

Formal test-case generation for UML statecharts

The unified modelling language has been introduced as a notation for modelling and reasoning about large and complex systems, and their design, across a wide range of application domains. System modelling and analysis techniques, especially those based on formal methods, are more and more used for enhancing traditional system engineering techniques for improving system quality. In particular this holds for model-based formal test case derivation using formal conformance testing. The contribution of the present paper is to provide a solid mathematical basis for conformance testing and automatic test case generation for UML statecharts (UMLSCs). We propose a formal conformance-testing relation for input-enabled transition systems with transitions labelled by input/output-pairs (IOLTSs). IOLTSs provide a suitable semantic model for a behavioural subset of UMLSCs. We also provide an algorithm which, for a UMLSC specification and the alphabet of implementations, generates a test suite. The algorithm is proven exhaustive and sound w.r.t. the conformance relation.

A Stochastic Causality-Based Process Algebra

This paper discusses stochastic extensions of a simple process algebra in a causality-based setting. Atomic actions are supposed to happen after a delay that is determined by a stochastic variable with a certain distribution. A simple stochastic type of event structures is discussed, restricting the distribution functions to be exponential. A corresponding operational semantics of this model is given and compared to existing (interleaved) approaches. Secondly, a stochastic variant of event structures is discussed where distributions are of a much more general nature, viz. of phase-type. This includes exponential, Erlang, Coxian and mixtures of exponential distributions.

Modular semantics for a UML statechart diagrams kernel and its extension to multicharts and branching time model-checking

Abstract Statechart diagrams provide a graphical notation to model dynamic aspects of system behaviour within the unified modelling language (UML). In this paper, we present a formal operational semantics for a behavioural subset of UML statechart diagrams (UMLSDs) including a formal proof of their correctness with respect to major UML semantics requirements concerning behavioural issues. We show how the modularity of our semantics definition can be exploited to define extensions, in particular we show an extension to models composed of collections of communicating statechart diagrams, which we call multicharts. Finally we present all the conceptual issues related to building a tool for action based branching time model-checking, for the automatic verification of formal correctness of UML multicharts. The approach we propose preserves all the information necessary to report the results of model-checking in terms of the original UMLSD specification. The reference verification environment used for this model-checking approach is JACK, where automata are represented in a standard format which facilitates the use of a collection of tools for automatic verification.

Formal modeling and quantitative analysis of KLAIM-based mobile systems

KLAIM is an experimental language designed for modeling and programming distributed systems composed of mobile components where distribution awareness and dynamic system architecture configuration are key issues. In this paper we propose STOCKLAIM, a STOchastic extension of cKLAIM, the core subset of KLAIM. cKLAIM includes process distribution, process mobility, and asynchronous communication. The extension makes it possible to integrate the modeling of quantitative aspects of mobile systems--- e.g. performance---with the functional specification of such systems. We present a formal operational semantics of STOcKLAIM, which associates a labeled transition system to each STOcKLAIM network and a translation to Continuous Time Markov Chains for quantitative analysis. We also show how STOcKLAIM can be used by means of a simple example, i.e. the modeling of the spreading of a virus.

Rate-Based Transition Systems for Stochastic Process Calculi

A variant of Rate Transition Systems (RTS), proposed by Klin and Sassone, is introduced and used as the basic model for defining stochastic behaviour of processes. The transition relation used in our variant associates to each process, for each action, the set of possible futures paired with a measure indicating their rates. We show how RTS can be used for providing the operational semantics of stochastic extensions of classical formalisms, namely CSP and CCS. We also show that our semantics for stochastic CCS guarantees associativity of parallel composition. Similarly, in contrast with the original definition by Priami, we argue that a semantics for stochastic *** -calculus can be provided that guarantees associativity of parallel composition.

On Specifying Real-Time Systems in a Causality-Based Setting

Event structures are a prominent noninterleaving model for concurrency. Real-time event structures associate a set of time instants to events, modelling absolute time constraints, and to causal dependencies, modelling relative delays between causally dependent events. We introduce this novel temporal model and show how it can be used to provide a denotational semantics to a real-time variant of a process algebra akin to LOTOS. This formalism includes a timed-action prefix which constrains the occurrence time of actions, a timeout and watchdog (i.e., timed interrupt) operator. An event-based operational semantics for this formalism is presented that is shown to be consistent with the denotational semantics. As an example we use an infinite buffer with time constraints on the message latency and the rates of accepting and producing data.

Metric semantics for true concurrent real time

This paper investigates the use of a complete metric space framework for providing denotational semantics to a real-time process algebra. The study is carried out in a non-interleaving setting and is based on a timed extension of Langeraks bundle event structures, a variant of Winskels event structures. The distance function is based on the amount of time to which event structures do ‘agree’. We show that this intuitive notion of distance is a pseudo metric (but not a metric) on the set of timed event structures. A generalisation to equivalence classes of timed event structures in which we abstract from event names and non-executable events (events that can never appear) is shown to be a complete ultra-metric space. We show that the resulting metric semantics is an abstraction of an existing cpo-based denotational and a related operational semantics for the considered language.

A formal testing framework for UML statechart diagrams behaviours: from theory to automatic verification

We propose a formal testing framework for a behavioural subset of UML statechart diagrams (UMLSDs). A formal operational semantics is defined, which uses the same core semantics introduced in Latella et al. (1999) but which is better suited for testing theory. The new semantics is proved consistent with our original one and is guaranteed to generate only finite state machines. Proper testing pre-orders and equivalences are defined which allow us to equate/distinguish systems on the basis of their interaction with the surrounding environment, abstracting from their internal structure. Finally, we provide a way for effective automatic verification of testing equivalence of our statecharts, based on existing techniques and tools.