Giorgio Bacci | Aalborg University (original) (raw)

Papers by Giorgio Bacci

Lecture Notes in Computer Science, 2014

Wide reactive systems are rewriting systems specified by wide reaction rules, where redex and rea... more Wide reactive systems are rewriting systems specified by wide reaction rules, where redex and reactum are lists of terms (forests), i.e. rules of the form l1(x1), . . . , ln(xn) ⇒ r1(y1), . . . , rn(yn) such that ∪iyi ⊆ ∪ixi. Wide reaction rules are particularly useful for process calculi for mobile and global computations, because they allow one to connect processes which can be at different places in the system, possibly crossing boundaries and firewalls. For instances, remote procedure calls can be modeled as a process in place i activating a reaction in a different place j; code mobility can be modeled by instantiating variables in yi with terms using variables from xj, for a different j; etc. In order to apply a wide reaction rule, we have to find a matching of the rule redex within the global state. This problem can be restated as follows: how to match a given forest (the redex) inside an unordered tree (the system), possibly finding the subtrees to be grafted at the forest's leaves (i.e., instantiating the variables)? We show that, although the problem is NP-complete in general, the exponential explosion depends only on the number n of roots of the forest (the width of the redex), and not on the size of the global tree (the system state). In most practical cases, the width is constant and small (i.e., ≤ 3), hence our results show that the wide reaction systems can be actually used for process calculi.

Electronic Proceedings in Theoretical Computer Science, 2009

We introduce the BioBeta Framework, a meta-model for both protein-level and membrane-level intera... more We introduce the BioBeta Framework, a meta-model for both protein-level and membrane-level interactions of living cells. This formalism aims to provide a formal setting where to encode, compare and merge models at different abstraction levels; in particular, higher-level (e.g. membrane) activities can be given a formal biological justification in terms of low-level (i.e., protein) interactions. A BioBeta specification provides a protein signature together a set of protein reactions, in the spirit of the kappa-calculus. Moreover, the specification describes when a protein configuration triggers one of the only two membrane interaction allowed, that is "pinch" and "fuse". In this paper we define the syntax and semantics of BioBeta, analyse its properties, give it an interpretation as biobigraphical reactive systems, and discuss its expressivity by comparing with kappa-calculus and modelling significant examples. Notably, BioBeta has been designed after a bigraphical metamodel for the same purposes. Hence, each instance of the calculus corresponds to a bigraphical reactive system, and vice versa (almost). Therefore, we can inherith the rich theory of bigraphs, such as the automatic construction of labelled transition systems and behavioural congruences.

In this paper we propose two behavioral distances that support approximate reasoning on Stochasti... more In this paper we propose two behavioral distances that support approximate reasoning on Stochastic Markov Models (SMMs), that are continuous-time stochastic transition systems where the residence time on each state is described by a generic probability measure on the positive real line. In particular, we study the problem of measuring the behavioral dissimilarity of two SMMs against linear real-time specifications expressed as Metric Temporal Logic (MTL) formulas or Deterministic Timed-Automata (DTA). The most natural choice for such a distance is the one that measures the maximal difference that can be observed comparing two SMMs with respect to their probability of satisfying an arbitrary specification. We show that computing this metric is NP-hard. In addition, we show that any algorithm that approximates the distance within a certain absolute error, depending on the size of the SMMs, is NP-hard. Nevertheless, we introduce an alternative distance, based on the Kantorovich metric, that is an over-approximation of the former and we show that, under mild assumptions on the residence time distributions, it can be computed in polynomial time.

ABSTRACT This paper presents a library for exactly computing the bisimilarity Kantorovich-based p... more ABSTRACT This paper presents a library for exactly computing the bisimilarity Kantorovich-based pseudometrics between Markov chains and between Markov decision processes. These are distances that measure the behavioral discrepancies between non-bisimilar systems. They are computed by using an on-the-fly greedy strategy that prevents the exhaustive state space exploration and does not require a complete storage of the data structures. Tests performed on a consistent set of (pseudo)randomly generated instances show that our algorithm improves the efficiency of the previously proposed iterative algorithms, on average, with orders of magnitude. The tool is available as a Mathematica package library.

ABSTRACT We propose a general definition of composition operator on Markov Decision Processes wit... more ABSTRACT 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 with respect to 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.

Lecture Notes in Computer Science, 2014

ABSTRACT We introduce a notion of bisimulation on labelled Markov Processes over generic measurab... more ABSTRACT We introduce a notion of bisimulation on labelled Markov Processes over generic measurable spaces in terms of arbitrary binary relations. Our notion of bisimulation is proven to coincide with the coalgebraic definition of Aczel and Mendler in terms of the Giry functor, which associates with a measurable space its collection of (sub)probability measures. This coalgebraic formulation allows one to relate the concepts of bisimulation and event bisimulation of Danos et al. (i.e., cocongruence) by means of a formal adjunction between the category of bisimulations and a (full sub)category of cocongruences, which gives new insights about the real categorical nature of their results. As a corollary, we obtain sufficient conditions under which state and event bisimilarity coincide.

ABSTRACT This paper proposes an algorithm for exact computation of bisimilarity distances between... more ABSTRACT This paper proposes an algorithm for exact computation of bisimilarity distances between discrete-time Markov chains introduced by Desharnais et. al. Our work is inspired by the theoretical results presented by Chen et al. at FoSSaCS'12, proving that these distances can be computed in polynomial time using the ellipsoid method. Despite its theoretical importance, the ellipsoid method is known to be inefficient in practice. To overcome this problem, we propose an efficient on-the-fly algorithm which, unlike other existing solutions, computes exactly the distances between given states and avoids the exhaustive state space exploration. It is parametric in a given set of states for which we want to compute the distances. Our technique successively refines over-approximations of the target distances using a greedy strategy which ensures that the state space is further explored only when the current approximations are improved. Tests performed on a consistent set of (pseudo)randomly generated Markov chains shows that our algorithm improves, on average, the efficiency of the corresponding iterative algorithms with orders of magnitude.

We propose a probabilistic interpretation of a class of reversible communicating processes. The r... more 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 ). This implies that such processes hit a success state in finite average time, if there is one.

Electronic Proceedings in Theoretical Computer Science, 2009

We present a bigraphical framework suited for modeling biological systems both at protein level a... more 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 kappa-calculus. Membrane-level interactions are represented by just two general rules, whose application can be triggered by protein-level interactions in a well-de\"ined 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.

Electronic Notes in Theoretical Computer Science, Nov 10, 2008

The Brane Calculus is a calculus intended to model the structure and the dynamics of biological m... more The Brane Calculus is a calculus intended to model the structure and the dynamics of biological membranes. In order to express properties of systems in this calculus, in previous work we have introduced a temporal-spatial logic called Brane Logic. A natural question of great practical importance is if model checking of this logic is decidable, that is, if it is possible to check automatically whether a given system satisfies a given formula. We have already shown that model checking is decidable for replication-free systems and guarantee-free formulas. In this paper, we show that admitting replication in systems, or any guarantee constructor in formulas (and quantifiers), leads model checking to be undecidable. Moreover, we give also a correspondence result between membranes and systems, showing that any system can be obtained by a canonical one where all information are contained on a membrane enclosing an empty compartment.

Coalgebraic Methods in Computer Science, 2012

We consider the problem of modeling syntax and semantics of probabilistic processes with continuo... more 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. To this end, we solve several problems. In particular, the format has to specify how to compose the semantics of processes (which basically are continuous state Markov processes). This is achieved by defining a language of measure terms, i.e., expressions specifically designed for describing probabilistic measures. Thus, the transition relation associates processes with measure terms. As an example application, we model a CCS-like calculus of processes placed in an Euclidean space. The approach we follow in this case can be readily adapted to other quantitative aspects, e.g. Quality of Service, physical and chemical parameters in biological systems, etc.

Arxiv preprint arXiv:1011.0488, Nov 2, 2010

We give a stochastic extension of the Brane Calculus, along the lines of recent work by Cardelli ... more We give a stochastic extension of the Brane Calculus, along the lines of recent work by Cardelli and Mardare [8]. In this presentation, the semantics of a Brane process is a measure of the stochastic distribution of possible derivations. To this end, we first introduce a labelled transition system for Brane Calculus, proving its adequacy w.r.t. the usual reduction semantics. Then, brane systems are presented 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 a SOS presentation of this stochastic semantics, which is compositional and syntax-driven. * Work funded by MIUR PRIN project "SisteR", prot. 20088HXMYN.

Arxiv preprint arXiv:0911.4513, Nov 23, 2009

We introduce the Bioβ Framework, a meta-model for both protein-level and membrane-level interacti... more We introduce the Bioβ Framework, a meta-model for both protein-level and membrane-level interactions of living cells. This formalism aims to provide a formal setting where to encode, compare and merge models at different abstraction levels; in particular, higher-level (e.g. membrane) activities can be given a formal biological justification in terms of low-level (i.e., protein) interactions.

Arxiv preprint arXiv:0911.4510, Nov 23, 2009

We present a bigraphical framework suited for modeling biological systems both at protein level a... more 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 κ-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.

Algebra and Coalgebra in Computer Science, 2009

Computational Methods in Systems Biology, 2006

In , Cardelli has proposed a schematic model of biological systems as three different and interac... more In , Cardelli has proposed a schematic model of biological systems as three different and interacting abstract machines. Following the approach pioneered in , these abstract machines are modelled using methodologies borrowed from the theory of concurrent systems.

Conference on Algebra and Coalgebra in Computer Science, 2009

Lecture Notes in Computer Science, 2014

Wide reactive systems are rewriting systems specified by wide reaction rules, where redex and rea... more Wide reactive systems are rewriting systems specified by wide reaction rules, where redex and reactum are lists of terms (forests), i.e. rules of the form l1(x1), . . . , ln(xn) ⇒ r1(y1), . . . , rn(yn) such that ∪iyi ⊆ ∪ixi. Wide reaction rules are particularly useful for process calculi for mobile and global computations, because they allow one to connect processes which can be at different places in the system, possibly crossing boundaries and firewalls. For instances, remote procedure calls can be modeled as a process in place i activating a reaction in a different place j; code mobility can be modeled by instantiating variables in yi with terms using variables from xj, for a different j; etc. In order to apply a wide reaction rule, we have to find a matching of the rule redex within the global state. This problem can be restated as follows: how to match a given forest (the redex) inside an unordered tree (the system), possibly finding the subtrees to be grafted at the forest's leaves (i.e., instantiating the variables)? We show that, although the problem is NP-complete in general, the exponential explosion depends only on the number n of roots of the forest (the width of the redex), and not on the size of the global tree (the system state). In most practical cases, the width is constant and small (i.e., ≤ 3), hence our results show that the wide reaction systems can be actually used for process calculi.

Electronic Proceedings in Theoretical Computer Science, 2009

We introduce the BioBeta Framework, a meta-model for both protein-level and membrane-level intera... more We introduce the BioBeta Framework, a meta-model for both protein-level and membrane-level interactions of living cells. This formalism aims to provide a formal setting where to encode, compare and merge models at different abstraction levels; in particular, higher-level (e.g. membrane) activities can be given a formal biological justification in terms of low-level (i.e., protein) interactions. A BioBeta specification provides a protein signature together a set of protein reactions, in the spirit of the kappa-calculus. Moreover, the specification describes when a protein configuration triggers one of the only two membrane interaction allowed, that is "pinch" and "fuse". In this paper we define the syntax and semantics of BioBeta, analyse its properties, give it an interpretation as biobigraphical reactive systems, and discuss its expressivity by comparing with kappa-calculus and modelling significant examples. Notably, BioBeta has been designed after a bigraphical metamodel for the same purposes. Hence, each instance of the calculus corresponds to a bigraphical reactive system, and vice versa (almost). Therefore, we can inherith the rich theory of bigraphs, such as the automatic construction of labelled transition systems and behavioural congruences.

In this paper we propose two behavioral distances that support approximate reasoning on Stochasti... more In this paper we propose two behavioral distances that support approximate reasoning on Stochastic Markov Models (SMMs), that are continuous-time stochastic transition systems where the residence time on each state is described by a generic probability measure on the positive real line. In particular, we study the problem of measuring the behavioral dissimilarity of two SMMs against linear real-time specifications expressed as Metric Temporal Logic (MTL) formulas or Deterministic Timed-Automata (DTA). The most natural choice for such a distance is the one that measures the maximal difference that can be observed comparing two SMMs with respect to their probability of satisfying an arbitrary specification. We show that computing this metric is NP-hard. In addition, we show that any algorithm that approximates the distance within a certain absolute error, depending on the size of the SMMs, is NP-hard. Nevertheless, we introduce an alternative distance, based on the Kantorovich metric, that is an over-approximation of the former and we show that, under mild assumptions on the residence time distributions, it can be computed in polynomial time.

ABSTRACT This paper presents a library for exactly computing the bisimilarity Kantorovich-based p... more ABSTRACT This paper presents a library for exactly computing the bisimilarity Kantorovich-based pseudometrics between Markov chains and between Markov decision processes. These are distances that measure the behavioral discrepancies between non-bisimilar systems. They are computed by using an on-the-fly greedy strategy that prevents the exhaustive state space exploration and does not require a complete storage of the data structures. Tests performed on a consistent set of (pseudo)randomly generated instances show that our algorithm improves the efficiency of the previously proposed iterative algorithms, on average, with orders of magnitude. The tool is available as a Mathematica package library.

ABSTRACT We propose a general definition of composition operator on Markov Decision Processes wit... more ABSTRACT 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 with respect to 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.

Lecture Notes in Computer Science, 2014

ABSTRACT We introduce a notion of bisimulation on labelled Markov Processes over generic measurab... more ABSTRACT We introduce a notion of bisimulation on labelled Markov Processes over generic measurable spaces in terms of arbitrary binary relations. Our notion of bisimulation is proven to coincide with the coalgebraic definition of Aczel and Mendler in terms of the Giry functor, which associates with a measurable space its collection of (sub)probability measures. This coalgebraic formulation allows one to relate the concepts of bisimulation and event bisimulation of Danos et al. (i.e., cocongruence) by means of a formal adjunction between the category of bisimulations and a (full sub)category of cocongruences, which gives new insights about the real categorical nature of their results. As a corollary, we obtain sufficient conditions under which state and event bisimilarity coincide.

ABSTRACT This paper proposes an algorithm for exact computation of bisimilarity distances between... more ABSTRACT This paper proposes an algorithm for exact computation of bisimilarity distances between discrete-time Markov chains introduced by Desharnais et. al. Our work is inspired by the theoretical results presented by Chen et al. at FoSSaCS'12, proving that these distances can be computed in polynomial time using the ellipsoid method. Despite its theoretical importance, the ellipsoid method is known to be inefficient in practice. To overcome this problem, we propose an efficient on-the-fly algorithm which, unlike other existing solutions, computes exactly the distances between given states and avoids the exhaustive state space exploration. It is parametric in a given set of states for which we want to compute the distances. Our technique successively refines over-approximations of the target distances using a greedy strategy which ensures that the state space is further explored only when the current approximations are improved. Tests performed on a consistent set of (pseudo)randomly generated Markov chains shows that our algorithm improves, on average, the efficiency of the corresponding iterative algorithms with orders of magnitude.

We propose a probabilistic interpretation of a class of reversible communicating processes. The r... more 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 ). This implies that such processes hit a success state in finite average time, if there is one.

Electronic Proceedings in Theoretical Computer Science, 2009

We present a bigraphical framework suited for modeling biological systems both at protein level a... more 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 kappa-calculus. Membrane-level interactions are represented by just two general rules, whose application can be triggered by protein-level interactions in a well-de\"ined 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.

Electronic Notes in Theoretical Computer Science, Nov 10, 2008

The Brane Calculus is a calculus intended to model the structure and the dynamics of biological m... more The Brane Calculus is a calculus intended to model the structure and the dynamics of biological membranes. In order to express properties of systems in this calculus, in previous work we have introduced a temporal-spatial logic called Brane Logic. A natural question of great practical importance is if model checking of this logic is decidable, that is, if it is possible to check automatically whether a given system satisfies a given formula. We have already shown that model checking is decidable for replication-free systems and guarantee-free formulas. In this paper, we show that admitting replication in systems, or any guarantee constructor in formulas (and quantifiers), leads model checking to be undecidable. Moreover, we give also a correspondence result between membranes and systems, showing that any system can be obtained by a canonical one where all information are contained on a membrane enclosing an empty compartment.

Coalgebraic Methods in Computer Science, 2012

We consider the problem of modeling syntax and semantics of probabilistic processes with continuo... more 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. To this end, we solve several problems. In particular, the format has to specify how to compose the semantics of processes (which basically are continuous state Markov processes). This is achieved by defining a language of measure terms, i.e., expressions specifically designed for describing probabilistic measures. Thus, the transition relation associates processes with measure terms. As an example application, we model a CCS-like calculus of processes placed in an Euclidean space. The approach we follow in this case can be readily adapted to other quantitative aspects, e.g. Quality of Service, physical and chemical parameters in biological systems, etc.

Arxiv preprint arXiv:1011.0488, Nov 2, 2010

We give a stochastic extension of the Brane Calculus, along the lines of recent work by Cardelli ... more We give a stochastic extension of the Brane Calculus, along the lines of recent work by Cardelli and Mardare [8]. In this presentation, the semantics of a Brane process is a measure of the stochastic distribution of possible derivations. To this end, we first introduce a labelled transition system for Brane Calculus, proving its adequacy w.r.t. the usual reduction semantics. Then, brane systems are presented 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 a SOS presentation of this stochastic semantics, which is compositional and syntax-driven. * Work funded by MIUR PRIN project "SisteR", prot. 20088HXMYN.

Arxiv preprint arXiv:0911.4513, Nov 23, 2009

We introduce the Bioβ Framework, a meta-model for both protein-level and membrane-level interacti... more We introduce the Bioβ Framework, a meta-model for both protein-level and membrane-level interactions of living cells. This formalism aims to provide a formal setting where to encode, compare and merge models at different abstraction levels; in particular, higher-level (e.g. membrane) activities can be given a formal biological justification in terms of low-level (i.e., protein) interactions.

Arxiv preprint arXiv:0911.4510, Nov 23, 2009

We present a bigraphical framework suited for modeling biological systems both at protein level a... more 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 κ-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.

Algebra and Coalgebra in Computer Science, 2009

Computational Methods in Systems Biology, 2006

In , Cardelli has proposed a schematic model of biological systems as three different and interac... more In , Cardelli has proposed a schematic model of biological systems as three different and interacting abstract machines. Following the approach pioneered in , these abstract machines are modelled using methodologies borrowed from the theory of concurrent systems.

Conference on Algebra and Coalgebra in Computer Science, 2009