We introduce Genetic Systems, a formalism inspired by genetic regulatory networks and suitable for modeling the interactions between the genes and the proteins, acting as regulatory products. The generation of new objects, representing proteins, is driven by genetic gates: a new object is produced when all the activator objects are available in the system, and no inhibitor object is available. Activators are not consumed by the application of such an evolution rule. Objects disappear because of degradation: each object is equipped with a lifetime, and the object decays when such a lifetime expires. We investigate the computational expressiveness of Genetic Systems: we show that they are Turing equivalent by providing encodings of Random Access Machines in Genetic Systems.

In this paper, we describe a new representation for deterministic rational-valued P systems that allows us to form a bridge between membrane computing and linear algebra. On the one hand, we prove that an efficient computation for these P systems can be described using linear algebra techniques. In particular, we show that the computation for getting a configuration in such P systems can be carried out by multiplying appropriate matrices. On the other hand, we also show that membrane computing techniques can be used to get the n th power of a given matrix.

The aim of the research domain known as process mining is to use process discovery to construct a process model as an abstract representation of event logs. The goal is to build a model (in terms of a Petri net) that can reproduce the logs under consideration, and does not allow different behaviours compared with those shown in the logs. In particular, process mining aims to verify the accuracy of the model design (represented as a Petri net), basically checking whether the same net can be rediscovered. However, the main mining methods proposed in the literature have some drawbacks: the classical α-algorithm is unable to rediscover various nets, while the region-based approach, which can mine them correctly, is too complex. In this paper, we compare different approaches and propose some ideas to counter the weaknesses of the region-based approach.

Several notions of non-interference have been proposed in the literature for studying the problem of confidentiality in concurrent systems. The common feature of these non-interference properties is that they are all defined as extensional properties based on some notion of behavioural equivalence on systems. Here, instead, we address the problem of defining non-interference by looking at the structure of the systems under investigation. We use a simple class of Petri nets, namely, contact-free elementary net systems, as the system model and define structural non-interference properties based on the absence of particular places in the net: such places show that a suitable causality or conflict relation is present between a high-level transition and a low-level one. We characterise one structural property, called PBNI+, which we show to be equivalent to the well-known behavioural property SBNDC. It essentially captures all the positive information flows (that is, a low-level user can deduce that some high-level action has occurred). We start by providing a characterisation of PBNI+ on contact-free elementary net systems, then extend the definition to cope with the richer class of trace nets.

We consider the structure of the intestinal epithelial tissue and of cell–cell junctions as the biological model inspiring a new class of P systems. First we define the concept of cell polarity, a formal property derived from epithelial cells, which present morphologically and functionally distinct regions of the plasma membrane. Then we show two preliminary results for this new model of computation: on the theoretical side, we show that P systems with cell polarity are computationally (Turing) complete; on the modelling side, we show that the transepithelial movement of glucose from the intestinal lumen into the blood can be described by such a formal system. Finally, we define tissue P systems with cell polarity, where each cell has fixed connections to the neighbouring cells and to the environment, according to both the cell polarity and specific cell–cell junctions.

The calculus of Mobile Ambients was proposed by Cardelli and Gordon as a foundational calculus for mobile computing. Since its introduction, the computational strength and the decidability of properties have been investigated for several fragments and variants of the standard calculus. We consider the problem of reachability and characterise a public (that is, restriction-free) fragment for which it is decidable. This fragment is obtained by removing the open capability and restricting the application of the replication operator to guarded processes only. This decidability result may appear surprising in combination with the fact that the same fragment was shown to be Turing complete by Maffeis and Phillips. Finally, we extend our decidability result in two ways: we first prove the decidability of a more general property called target reachability (according to which the target of interest for the reachability analysis consists of a possibly infinite set of processes) and then show that our decidability results also hold for a more general calculus, which includes the sophisticated communication mechanisms of Boxed Ambients, which is the most relevant variant of Mobile Ambients without the open capability.

Genetic Systems are a formalism inspired by genetic regulatory networks, suitable for modeling the interactions between genes and proteins, acting as regulatory products. The evolution is driven by genetic gates: a new object (representing a protein) is produced when all activator objects are available in the system, and no inhibitor object is present. Activators are not consumed by the application of such a rule. Objects disappear because of degradation: each object is equipped with a lifetime, and the object decays when such a lifetime expires.It is known that such systems are Turing powerful, either when we consider interleaving semantics (a single action is executed in each computational step) as well as if we consider maximal parallel semantics (all the rules that can be applied at a computational step must be applied). In this paper we investigate the power of inhibiting rules.

The application of concurrent calculi to the formalisation of biological systems constitutes a promising approach to the analysis of biological phenomena in silico. The peculiar nature of such systems inspired the introduction of specific features in biologically-oriented calculi, such as compartments to model more faithfully their highly organised structure.In this paper we present S pi@, a conservative extension of the stochastic pi-calculus which allows an intuitive and concise formalisation of multi-compartment systems with dynamic structure, despite retaining the simplicity of the original pi-calculus. The possibility to encode into S pi@ several bio-inspired, compartmentalised languages demonstrates its expressive power and flexibility.The calculus is accompanied by an extended version of Gillespie's stochastic simulation algorithm, able to handle multiple compartments with varying volumes. An enhanced formalisation of the algorithm is also presented, in order to provide efficient simulation in the presence of a high number of compartments and reactions. (C) 2009 Elsevier B.V. All rights reserved.

Priority is a frequently used feature of many computational systems. In this paper we study the expressiveness of two process algebras enriched with different priority mechanisms. In particular, we consider a finite (that is, recursion-free) fragment of asynchronous CCS with global priority (FAP, for short) and Phillips' CPG (CCS with local priority), and contrast their expressive power with that of two non-prioritised calculi, namely the π-calculus and its broadcast-based version, called bπ. We prove, by means of leader-election-based separation results, that, under certain conditions, there exists no encoding of FAP in π-Calculus or CPG. Moreover, we single out another problem in distributed computing, which we call the last man standing problem (LMS for short), that better reveals the gap between the two prioritised calculi above and the two non-prioritised ones, by proving that there exists no parallel-preserving encoding of the prioritised calculi in the non-prioritised calculi retaining any sincere (complete but partially correct, that is, admitting divergence or premature termination) semantics.

In this paper we investigate the expressive power of three alternative approaches to the definition of infinite behaviours in process calculi, namely, recursive definitions, replication and iteration. We prove several results discriminating between the calculi obtained from a core CCS by adding the three mechanisms mentioned above. These results are derived by considering the decidability of four basic properties: termination (that is, all computations are finite); convergence (that is, the existence of a finite computation); barb (that is, the ability to perform an action on a given channel) and weak bisimulation.Our results, which are summarised in Table 1, show that the three calculi form a strict expressiveness hierarchy in that: all the properties mentioned are undecidable in CCS with recursion; only termination and barb are decidable in CCS with replication; all the properties are decidable in CCS with iteration.As a corollary, we also obtain a strict expressiveness hierarchy with respect to weak bisimulation, since there exist weak bisimulation preserving encodings of iteration in replication and of replication in recursion, whereas there are no weak bisimulation preserving encodings in the other directions.

A distributed model for the π-calculus is presented in terms of Place/Transition Petri nets with inhibitor arcs (PTI for short). Such a class of nets is equipped with a step and a causal semantics, hence allowing to study non-interleaving semantics for the π-calculus. We show the correctness of the semantics by proving that the interleaving semantics induced by the PTI semantics is fully abstract with respect to the interleaving early semantics originally defined in terms of labelled transition systems. We also argue the impossibility to define reasonable distributed semantics that preserve the intended non-interleaving semantics if we simply use Place/Transition nets without inhibitor arcs. Some decidability results (notably, the satisfaction of linear time μ-calculus formulae) are presented for the subclass of the π-calculus generating finite PTI nets.

The application of concurrent calculi to the formalisation of biological systems constitutes a promising approach to the analysis in silico of biological phenomena. The Gillespie algorithm is one of the main models exploited for their stochastic simulation. While the original algorithm considers only one fixed-volume compartment, the simulation of biological systems often requires multi-compartment semantics. In this paper we present an enhanced formulation of an extended version of the algorithm which handles multiple compartments with varying volumes. The presented algorithm is used as basis for the implementation of an extension of the stochastic π-Calculus, called Sπ@, which allows an intuitive and concise formalisation of such systems. The algorithm is also efficient in presence of a high number of compartments and reactions, therefore Sπ@ represents the starting point for the development of an effective tool for the simulation of biological systems with dynamical structure even in presence of computationally expensive phenomena like diffusion.

Brane calculi are a family of biologically inspired process calculi proposed in [L. Cardelli. Brane Calculi - Interactions of biological membranes. In Proc. Computational Methods in System Biology 2004 (CMSB 2004), LNCS 3082, Springer, 2005] for modeling the interactions of dynamically nested membranes. In [L. Cardelli. Brane Calculi - Interactions of biological membranes. In Proc. Computational Methods in System Biology 2004 (CMSB 2004), LNCS 3082, Springer, 2005] a basic calculus for membranes interactions – called Phago/Exo/Pino (PEP) – is proposed, whose primitives are inspired by endocytosis and exocytosis. An alternative basic calculus – called Mate/Bud/Drip (MBD) and inspired by membrane fusion and fission – is also outlined and shown to be encodable in Phago/Exo/Pino in [L. Cardelli. Brane Calculi - Interactions of biological membranes. In Proc. Computational Methods in System Biology 2004 (CMSB 2004), LNCS 3082, Springer, 2005]. In this paper we survey some results on the comparison of the expressivity of the PEP and the MBD calculi, w.r.t. their ability to act as computational devices.

P systems are a biologically inspired model introduced by Gheorghe Păun with the aim of representing the structure and the functioning of the cell. P systems are usually equipped with the maximal parallelism semantics; however, since their introduction, some alternative semantics have been proposed and investigated. We propose a semantics that describes the causal dependencies occurring between the reactions of a P system. We investigate the basic properties that are satisfied by such a semantics. The notion of causality turns out to be quite relevant for biological systems, as it permits to point out which events occurring in a biological pathway are necessary for another event to happen.

Genetic Systems are a formalism inspired by genetic regulatory networks, suitable for modeling the interactions between genes and proteins, acting as regulatory products. The evolution is driven by genetic gates: a new object (representing a protein) is produced when all activator objects are available in the system, and no inhibitor object is present. Activators are not consumed by the application of such a rule. Objects disappear because of degradation: each object is equipped with a lifetime, and the object decays when such a lifetime expires. We investigate the computational expressiveness of Genetic Systems with interleaving semantics (a single action is executed in a computational step): we show that they are Turing equivalent by providing a deterministic encoding of Random Access Machines in Genetic Systems. We also show that the computational power strictly decreases when moving to Genetic Systems where either the degradation or the inhibition mechanism are absent.

P systems are a biologically inspired model introduced by Gheorghe Nun with the aim of representing the structure and the functioning of the cell. Since their introduction, several variants of P systems have been proposed and explored.We concentrate on the class of catalytic P systems without priorities associated with the rules. We show that the theory of Well-Structured Transition Systems can be used to decide the divergence problem (i.e. checking for the existence of an infinite computation) for such a class of P systems.As a corollary, we obtain an alternative proof of the nonuniversality of deterministic catalytic P systems, an open problem recently solved by Ibarra and Yen. (c) 2007 Published by Elsevier B.V.

Brane Calculi are a family of biologically inspired process calculi, proposed in [6] to model the interactions of dynamically nested membranes. We propose a semantics that describes the causal dependencies occurring between the reactions of a system described in Brane Calculi. We investigate the basic properties that are satisfied by such a semantics. The notion of causality turns out to be quite relevant for biological systems, as it permits to point out which events occurring in a biological pathway are necessary for another event to happen.