Angelo Troina

Stochastic Bigraphs

In this paper we present a stochastic semantics for Bigraphical Reactive Systems. A reduction and a labelled stochastic semantics for bigraphs are defined. As a sanity check, we prove that the two semantics are consistent with each other. We illustrate the expressiveness of the framework with an example of membrane budding in a biological system.

Parametric probabilistic transition systems for system design and analysis

We develop a model of parametric probabilistic transition Systems (PPTSs), where probabilities associated with transitions may be parameters. We show how to find instances of the parameters that satisfy a given property and instances that either maximize or minimize the probability of reaching a certain state. As an application, we model a probabilistic non-repudiation protocol with a PPTS. The theory we develop allows us to find instances that maximize the probability that the protocol ends in a fair state (no participant has an advantage over the others).

Stochastic Calculus of Looping Sequences for the Modelling and Simulation of Cellular Pathways

The paper presents the Stochastic Calculus of Looping Sequences (SCLS) suitable to describe microbiological systems, such as cellular pathways, and their evolution. Systems are represented by terms. The terms of the calculus are constructed by basic constituent elements and operators of sequencing, looping, containment and parallel composition. The looping operator allows tying up the ends of a sequence, thus creating a circular sequence which can represent a membrane. The evolution of a term is modelled by a set of rewrite rules enriched with stochastic rates representing the speed of the activities described by the rules, and can be simulated automatically. As applications, we give SCLS representations of the regulation process of the lactose operon in Escherichia coli and of the quorum sensing in Pseudomonas aeruginosa . A prototype simulator (SCLSm) has been implemented in F# and used to run the experiments. A public version of the tool is available at the url: http://www.di.unipi.it/~milazzo/biosims/ .

Bisimulations in calculi modelling membranes

Bisimulations are well-established behavioural equivalences that are widely used to study properties of computer science systems. Bisimulations assume the behaviour of systems to be described as labelled transition systems, and properties of a system can be verified by assessing its bisimilarity with a system one knows to enjoy those properties.In this paper we show how semantics based on labelled transition systems and bisimulations can be defined for two formalisms for the description of biological systems, both capable of describing membrane interactions. These two formalisms are the Calculus of Looping Sequences (CLS) and Brane Calculi, and since they stem from two different approaches (rewrite systems and process calculi) bisimulation appears to be a good candidate as a general verification method.We introduce CLS and define a labelled semantics and bisimulations for which we prove some congruence results. We show how bisimulations can be used to verify properties by way of two examples: the description of the regulation of lactose degradation in Escherichia coli and the description of the EGF signalling pathway. We recall the PEP calculus (the simplest of Brane Calculi) and its translation into CLS, we define a labelled semantics and some bisimulation congruences for PEP processes, and we prove that bisimilar PEP processes are translated into bisimilar CLS terms.

Bisimulation congruences in the calculus of looping sequences

The Calculus of Looping Sequences (CLS) is a calculus suitable to describe biological systems and their evolution. CLS terms are constructed by starting from basic constituents and composing them by means of operators of concatenation, looping, containment and parallel composition. CLS terms can be transformed by applying rewrite rules. We give a labeled transition semantics for CLS by using, as labels, contexts in which rules can be applied. We define bisimulation relations that are congruences with respect to the operators on terms, and we show an application of CLS to the modeling of a biological system and we use bisimulations to reason about properties of the described system.

A probabilistic applied pi-calculus

We propose an extension of the Applied Pi-calculus by introducing nondeterministic and probabilistic choice operators. The semantics of the resulting model, in which probability and nondeterminism are combined, is given by Segalas Probabilistic Automata driven by schedulers which resolve the nondeterministic choice among the probability distributions over target states. Notions of static and observational equivalence are given for the enriched calculus. In order to model the possible interaction of a process with its surrounding environment a labeled semantics is given together with a notion of weak bisimulation which is shown to coincide with the observational equivalence. Finally, we prove that results in the probabilistic framework are preserved in a purely nondeterministic setting.

Weak bisimulation for probabilistic timed automata and applications to security

We are interested in describing timed systems that exhibit probabilistic behaviors. To this purpose, we define a model of probabilistic timed automata and give a concept of weak bisimulation together with an algorithm to decide it. We use this model for describing and analyzing a probabilistic non-repudiation protocol in a timed setting.

Design and verification of long-running transactions in a timed framework

Long-running transactions consist of tasks which may be executed sequentially and in parallel, may contain subtasks, and may require to be completed before a deadline. These transactions are not atomic and, in case of executions which cannot be completed, a compensation mechanism must be provided. In this paper we develop a model of Communicating Hierarchical Timed Automata suitable to describe the mentioned aspects in a framework where also time is taken into account. We develop the patterns for composing long-running transactions sequentially, in parallel or by nesting. The correct compensation of a composed long-running transaction is preserved by these composition patterns. The automaton-theoretic approach allows the verification of properties by model checking. As a case study, we model and analyse an example of e-commerce application described in terms of long-running transactions.

Type Disciplines for Analysing Biologically Relevant Properties

The calculus of looping sequences is a formalism for describing evolution of biological systems by means of term rewriting rules. We propose to enrich this calculus with type disciplines to guarantee the soundness of reduction rules with respect to interesting biological properties.

Stochastic Calculus of Wrapped Compartments

The Calculus of Wrapped Compartments (CWC) is a variant of the Calculus of Looping Sequences(CLS). While keeping the same expressiveness, CWC strongly simplifies the development of auto-matic tools for the analysis of biological systems. The main simplification consists in the removal ofthe sequencing operator, thus lightening the formal treatment of the patterns to be matched in a term(whose complexity in CLS is strongly affected by the variables matching in the sequences).We define a stochastic semantics for this new calculus. As an application we model the interac-tion between macrophages and apoptotic neutrophils and a mechanism of gene regulation in E.Coli.