Rom Langerak

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.

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.

A Complete Finite Prefix for Process Algebra

In this paper we show how to use McMillans complete finite prefix approach for process algebra. We present the model of component event structures as a semantics for process algebra, and show how to construct a complete finite prefix for this model. We present a simple adequate order (using an order on process algebra expressions) as an optimization to McMillans original algorithm.

Causal Ambiguity and Partial Orders in Event Structures

Event structure models often have some constraint which ensures that for each system run it is clear what are the causal predecessors of an event (i.e. there is no causal ambiguity). In this contribution we study what happens if we remove such constraints. We define five different partial order semantics that are intentional in the sense that they refer to syntactic aspects of the model. We also define an observational partial order semantics, that derives a partial order from just the event traces. It appears that this corresponds to the so-called early intentional semantics; the other intentional semantics cannot be observationally characterized. We study the equivalences induced by the different partial order definitions, and their interrelations.

A Consistent Causality-Based View on a Timed Process AlgebraIncluding Urgent Interactions

This paper discusses a timed variant of a process algebra akin to LOTOS, baptized UPA, in a causality-based setting. Two timed features are incorporated—a delay function which constrains the occurrence time of atomic actions and an urgency operator that forces (local or synchronized) actions to happen urgently. Timeouts are typical urgent phenomena. A novel timed extension of event structures is introduced and used as a vehicle to provide a denotational causality-based semantics for UPA. Recursion is dealt with by using standard fixpoint theory. In addition, an operational semantics is presented based on separate time- and action-transitions that is shown to be consistent with the event structure semantics. An interleaving semantics for UPA is immediately obtained from the operational semantics. By adopting this dual approach the well-developed timed interleaving view is extended with a consistent timed partial order view and a comparison is facilitated of the partial order model and the variety of existing (interleaved) timed process algebras.

Partial order models for quantitative extensions of LOTOS

Event structures are a prominent model for non-interleaving concurrency. The use of event structures for providing a compositional non-interleaving semantics to LOTOS without data is studied. In particular, several quantitative extensions of event structures are proposed that incorporate notions like time – both of deterministic and stochastic nature – and probability. The suitability of these models for giving a non-interleaving semantics to a timed, stochastic and probabilistic extension of LOTOS is investigated. Consistency between the event structure semantics and an (event-based) operational semantics is addressed for the different quantitative variants of LOTOS and is worked out for the timed case in more detail. These consistency results facilitate the coherent use of an interleaving and a non-interleaving semantic view in a single design trajectory and provide a justification for the event structure semantics. As a running example an infinite buffer is used in which gradually timing constraints on latency and rates of accepting and producing data and the probability of loss of messages are incorporated

Modeling Biological Pathway Dynamics With Timed Automata

Living cells are constantly subjected to a plethora of environmental stimuli that require integration into an appropriate cellular response. This integration takes place through signal transduction events that form tightly interconnected networks. The understanding of these networks requires capturing their dynamics through computational support and models. ANIMO (analysis of Networks with Interactive Modeling) is a tool that enables the construction and exploration of executable models of biological networks, helping to derive hypotheses and to plan wet-lab experiments. The tool is based on the formalism of Timed Automata, which can be analyzed via the UPPAAL model checker. Thanks to Timed Automata, we can provide a formal semantics for the domain-specific language used to represent signaling networks. This enforces precision and uniformity in the definition of signaling pathways, contributing to the integration of isolated signaling events into complex network models. We propose an approach to discretization of reaction kinetics that allows us to efficiently use UPPAAL as the computational engine to explore the dynamic behavior of the network of interest. A user-friendly interface hides the use of Timed Automata from the user, while keeping the expressive power intact. Abstraction to single-parameter kinetics speeds up construction of models that remain faithful enough to provide meaningful insight. The resulting dynamic behavior of the network components is displayed graphically, allowing for an intuitive and interactive modeling experience.

Correctness Preserving Transformations for the Early Phases of Software Development

The Lotosphere methodology is meant to support system designers and implementors along the trajectory from an initial, abstract specification, down to concrete design and implementation: the latter should be obtained from the former via a disciplined sequence of transformation and refinement steps.

Reachability Analysis of Stochastic Hybrid Systems by Optimal Control

For stochastic hybrid systems, the reachability analysis is an important and difficult problem. In this paper, we prove that, under natural assumptions, reachability analysis can be characterised as an optimal stopping problem. In this way, one can apply numerical methods from optimal control to solve the reachability verification problems.

Modelling biological pathway dynamics with Timed Automata

When analysing complex interaction networks occurring in biological cells, a biologist needs computational support in order to understand the effects of signalling molecules (e.g. growth factors, drugs). ANIMO (Analysis of Networks with Interactive MOdelling) is a tool that allows the user to create and explore executable models of biological networks, helping to derive hypotheses and to plan wet-lab experiments. The tool is based on the formalism of Timed Automata, which can be analysed via the UPPAAL model checker. Thanks to Timed Automata, we can provide a formal semantics for the domain-specific language used to represent signalling networks. This enforces precision and uniformity in the definition of signalling pathways, contributing to the integration of signalling event models into complex, crosstalk-driven networks. We propose an approach to discretization of reaction kinetics that allows us to efficiently use UPPAAL as the computational engine to explore the dynamic cell behaviour. A user friendly interface makes the use of Timed Automata completely transparent to the biologist, while keeping the expressive power intact. This allows to define relatively simple, yet faithful models of complex biological interactions. The resulting timed behaviour is displayed graphically, allowing for an intuitive and interactive modelling experience.