Giorgio Bacci

Computing Behavioral Distances, Compositionally

We propose a general definition of composition operator on Markov Decision Processes with rewards (MDPs) and identify a well behaved class of operators, called safe, that are guaranteed to be non-extensive w.r.t. the bisimilarity pseudometrics of Ferns et al. [10], which measure behavioral similarities between MDPs. For MDPs built using safe/non-extensive operators, we present the first method that exploits the structure of the system for (exactly) computing the bisimilarity distance on MDPs. Experimental results show significant improvements upon the non-compositional technique.

On the statistical thermodynamics of reversible communicating processes

We propose a probabilistic interpretation of a class of reversible communicating processes. The rate of forward and backward computing steps, instead of being given explicitly, is derived from a set of formal energy parameters. This is similar to the Metropolis-Hastings algorithm. We find a lower bound on energy costs which guarantees that a process converges to a probabilistic equilibrium state (a grand canonical ensemble in statistical physics terms [19]). This implies that such processes hit a success state in finite average time, if there is one.

DBtk: a toolkit for directed bigraphs

We present DBtk, a toolkit for Directed Bigraphs. DBtk supports a textual language for directed bigraphs, the graphical visualization of bigraphs, the calculation of IPO labels, and the calculation of redex matchings. Therefore, this toolkit provides the main functions needed to implement simulators and verification tools.

Modal logics for brane calculus

The Brane Calculus is a calculus of mobile processes, intended to model the transport machinery of a cell system. In this paper, we introduce the Brane Logic, a modal logic for expressing formally properties about systems in Brane Calculus. Similarly to previous logics for mobile ambients, Brane Logic has specific spatial and temporal modalities. Moreover, since in Brane Calculus the activity resides on membrane surfaces and not inside membranes, we need to add a specific logic (akin Hennessy-Milner’s) for reasoning about membrane activity. We present also a proof system for deriving valid sequents in Brane Logic. Finally, we present a model checker for a decidable fragment of this logic.

Measurable stochastics for Brane Calculus

The main aim of this work is to give a stochastic extension of the Brane Calculus, along the lines of recent work by Cardelli and Mardare (2010) [12]. In this approach, the semantics of a process is a measure of the stochastic distribution of possible derivations. To this end, we first introduce a compositional, finitely branching labelled transition system for Brane Calculus; interestingly, the associated strong bisimulation is a congruence. Then, we give a stochastic semantics to Brane systems by defining them as Markov processes over the measurable space generated by terms up-to syntactic congruence, and where the measures are indexed by the actions of this new LTS. Finally, we provide an SOS presentation of this stochastic semantics, which is compositional and syntax-driven, and moreover the induced rate bisimilarity is a congruence.

Bigraphical models for protein and membrane interactions

We present a bigraphical framework suited for modeling biological systems both at protein level and at membrane level. We characterize formally bigraphs corresponding to biologically meaningful systems, and bigraphic rewriting rules representing biologically admissible interactions. At the protein level, these bigraphic reactive systems correspond exactly to systems of k-calculus. Membrane-level interactions are represented by just two general rules, whose application can be triggered by proteinlevel interactions in a well-defined and precise way. This framework can be used to compare and merge models at different abstraction levels; in particular, higher-level (e.g. mobility) activities can be given a formal biological justification in terms of low-level (i.e., protein) interactions. As examples, we formalize in our framework the vesiculation and the phagocytosis processes. Cardelli in [8] has convincingly argued that the various biochemical toolkits identified by biologists can be described as a hierarchy of abstract machines, each of which can be modelled using methods and techniques from concurrency theory. These machines are highly interdependent: “to understand the functioning of a cell, one must understand also how the various machines interact” [8]. Like other complex situations, it seems unlikely to find a single notation covering all aspects of a whole organism. In fact, we are in presence of a tower of models [19], each focusing on specific aspects of the biological system, at different levels of abstractions. Higher-level models must be represented, orrealised, at a lower level, and where possible this representation must be proved sound; in addition, we need to combine different models at the same level. To this end, we need a general metamodel, that is, a framework, where these models (possibly at different abstraction levels) can be encoded, and their interactions can be formally described. In this paper, we substantiate Milner’s idea that bigraphs can be successfully used as a framework for systems biology. More precisely, we define a class of biological bigraphs, and biological bigraphical reactive systems (BioRS), for dealing with both protein-level and membrane-level interactions. An important design choice is that this framework has to be biologically sound, i.e., it must admit only systems and reactions which are biologically meaningful, especially at lower level machines (i.e. protein). In this way, encoding a given model, for any abstract machine, as a BioRS provides automatically a formal, biologically sound justification for the model (or “implementation”) in terms of protein reactions and explains how its membrane-level interactions are realised by protein machinery. In order to formalize this “biological soundness”, we need a formal protein model to compare to our framework. We choose Danos and Laneve’s k-calculus, one of the most accepted formal model of protein systems. By suitable sorting conditions, we define a bigraphical framework which allows all and only protein configurations and interactions of the k-calculus. It is important to notice, however, that our methodology is general, and can be applied to other formal protein models. On the other hand, membrane nesting reconfiguration can be performed by just only two general rules, corresponding to the natural phenomena of “pinch” and “fuse” [10]. For encoding a given membrane model one has just to refine this general schema by specifying when these reactions are triggered,

Structural Operational Semantics for Continuous State Probabilistic Processes

We consider the problem of modeling syntax and semantics of probabilistic processes with continuous states (e.g. with continuous data). Syntax and semantics of these systems can be defined as algebras and coalgebras of suitable endofunctors over Meas, the category of measurable spaces. In order to give a more concrete representation for these coalgebras, we present an SOS-like rule format which induces an abstract GSOS over Meas; this format is proved to yield a fully abstract universal semantics, for which behavioural equivalence is a congruence.

On the Total Variation Distance of Semi-Markov Chains

Semi-Markov chains (SMCs) are continuous-time probabilistic transition systems where the residence time on states is governed by generic distributions on the positive real line.

Converging from Branching to Linear Metrics onźMarkov Chains

We study the strong and strutter trace distances on Markov chains MCs. Our interest in these metrics is motivated by their relation to the probabilistic