Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Stochastic reaction networks are a fundamental model to describe interactions between species whe... more Stochastic reaction networks are a fundamental model to describe interactions between species where random fluctuations are relevant. The master equation provides the evolution of the probability distribution across the discrete state space consisting of vectors of population counts for each species. However, since its exact solution is often elusive, several analytical approximations have been proposed. The deterministic rate equation (DRE) gives a macroscopic approximation as a compact system of differential equations that estimate the average populations for each species, but it may be inaccurate in the case of nonlinear interaction dynamics. Here we propose finite-state expansion (FSE), an analytical method mediating between the microscopic and the macroscopic interpretations of a stochastic reaction network by coupling the master equation dynamics of a chosen subset of the discrete state space with the mean population dynamics of the DRE. An algorithm translates a network into ...
We propose a novel approach to the statistical analysis of simulation models and, especially, age... more We propose a novel approach to the statistical analysis of simulation models and, especially, agent-based models (ABMs). Our main goal is to provide a fully automated and model-independent tool-kit to inspect simulations and perform counter-factual analysis. Our approach: (i) is easy-to-use by the modeller, (ii) improves reproducibility of results, (iii) optimizes running time given the modeller’s machine, (iv) automatically chooses the number of required simulations and simulation steps to reach user-specified statistical confidence, and (v) automatically performs a variety of statistical tests. In particular, our framework is designed to distinguish the transient dynamics of the model from its steady state behaviour (if any), estimate properties of the model in both “phases”, and provide indications on the ergodic (or non-ergodic) nature of the simulated processes – which, in turns allows one to gauge the reliability of a steady state analysis. Estimates are equipped with statisti...
The problem of comparison and minimization for ordinary differential equations (ODEs) through beh... more The problem of comparison and minimization for ordinary differential equations (ODEs) through behavioral equivalences has been tackled so far using exact notions. However these may not be robust enough in practice because they are highly sensitive to the specific choice of parameters. We study ODEs with polynomial derivatives of any degree, covering linear/affine systems and chemical reaction networks with mass-action kinetics. For this class, we introduce approximate differential equivalence as a more permissive notion that allows variables of an ODE system to be related even if they vary in their parameters up to a given tolerance. We develop algorithms to (i) compute the largest approximate differential equivalence, (ii) construct a quotient approximate model from the original one via an appropriate perturbation of the parameters, and (iii) provide a formal certificate on the quality of the approximation. Finally, we apply approximate differential equivalences for symmetry reduct...
BPMN collaboration models have acquired increasing relevance in software development since they s... more BPMN collaboration models have acquired increasing relevance in software development since they shorten the communication gap between domain experts and IT specialists and permit clarifying the characteristics of software systems needed to provide automatic support for the activities of complex organisations. Nonetheless, the lack of effective formal verification capabilities can hinder the full adoption of the BPMN standard by IT specialists, as it prevents precisely check the satisfaction of behavioural properties, with negative impacts on the quality of the software. To address these issues, this paper proposes BProVe, a novel verification approach for BPMN collaborations. This combines both standard model checking techniques, through the MAUDE’s LTL model checker, and statistical model checking techniques, through the statistical analyser MULTIVESTA. The latter makes BProVe effective also on those scenarios suffering from the state-space explosion problem, made even more acute b...
The ASCENS project deals with designing systems as ensembles of adaptive components. Among the ou... more The ASCENS project deals with designing systems as ensembles of adaptive components. Among the outputs of the ASCENS project are multiple tools that address particular issues in designing the ensembles, ranging from support for early stage formal modeling to runtime environment for executing and monitoring ensemble implementations. The goal of this chapter is to provide a compact description of the individual tools, which is supplemented by additional downloadable material on the project website.
One of the most distinctive features of collective adaptive systems (CAS) is the presence of many... more One of the most distinctive features of collective adaptive systems (CAS) is the presence of many individuals which interact with each other and with the environment, giving rise to a system-level behaviour that cannot be analyzed by studying the single agents in isolation. The interaction structure among the individuals of CAS is often captured by networks where nodes denote individuals and edges interactions. Understanding the interplay between the network topology and the CAS dynamics calls for tools from network theory in order, for instance, to identify the most important nodes of a network. Centrality measures address this task by assigning an importance measure to each node, a possible example being the famous PageRank algorithm of Google. In this paper we investigate the relationship between centrality measures and model reduction techniques, such as lumpability of Markov chains, which seek to reduce a model into a smaller one that can be processed more efficiently, while pr...
CARMA (Collective Adaptive Resource-sharing Markovian Agents) is a process-algebra-based quantita... more CARMA (Collective Adaptive Resource-sharing Markovian Agents) is a process-algebra-based quantitative language developed for the modeling of collective adaptive systems. A CARMA model consists of an environment in which a collective of components with attribute stores interact via unicast and broadcast communication, providing a rich modeling formalism. The semantics of a CARMA model are given by a continuous-time Markov chain which can be simulated using the CARMA Eclipse Plug-in. Furthermore, statistical model checking can be applied to the trajectories generated through simulation using the MultiVeStA tool. This advanced tutorial will introduce some of the theory behind CARMA and MultiVeStA as well as demonstrate its application to collective adaptive system modeling.
Domain-specific quantitative modeling and analysis approaches are fundamental in scenarios in whi... more Domain-specific quantitative modeling and analysis approaches are fundamental in scenarios in which qualitative approaches are inappropriate or unfeasible. In this paper, we present a tool-supported approach to quantitative graph-based security risk modeling and analysis based on attack-defense trees. Our approach is based on QFLan , a successful domain-specific approach to support quantitative modeling and analysis of highly configurable systems, whose domain-specific components have been decoupled to facilitate the instantiation of the QFLan approach in the domain of graph-based security risk modeling and analysis. Our approach incorporates distinctive features from three popular kinds of attack trees, namely enhanced attack trees, capabilities-based attack trees and attack countermeasure trees, into the domain-specific modeling language. The result is a new framework, called RisQFLan , to support quantitative security risk modeling and analysis based on attack-defense diagrams. B...
We introduce polynomial couplings, a generalization of probabilistic couplings, to develop an alg... more We introduce polynomial couplings, a generalization of probabilistic couplings, to develop an algorithm for the computation of equivalence relations which can be interpreted as a lifting of probabilistic bisimulation to polynomial differential equations, a ubiquitous model of dynamical systems across science and engineering. The algorithm enjoys polynomial time complexity and complements classical partition-refinement approaches because: (a) it implements a local exploration of the system, possibly yielding equivalences that do not necessarily involve the inspection of the whole system of differential equations; (b) it can be enhanced by up-to techniques; and (c) it allows the specification of pairs which ought not be included in the output. Using a prototype, these advantages are demonstrated on case studies from systems biology for applications to model reduction and comparison. Notably, we report four orders of magnitude smaller runtimes than partition-refinement approaches when ...
This short paper summarises the contributions published in [4], where we introduce QFLan, a frame... more This short paper summarises the contributions published in [4], where we introduce QFLan, a framework for quantitative modeling and analysis of highly (re)configurable systems, like software product lines. We define a rich domain specific language (DSL) for systems with variability in terms of features, which can be dynamically installed, removed or replaced, capable of modeling probabilistic behavior, possibly subject to quantitative feature constraints. High-level DSL specifications are automatically encoded in a process algebra whose operational behavior interacts with a store of constraints, which allows to separate a system’s configuration from its behavior. The resulting probabilistic configurations and behavior converge seamlessly in a semantics based on discrete-time Markov chains, thus enabling quantitative analysis. An accompanying Eclipse-based tool offers a modern integrated development environment to specify such systems and to perform analyses that range from the likel...
Stochastic reaction networks are a fundamental model to describe interactions between species whe... more Stochastic reaction networks are a fundamental model to describe interactions between species where random fluctuations are relevant. The master equation provides the evolution of the probability distribution across the discrete state space consisting of vectors of population counts for each species. However, since its exact solution is often elusive, several analytical approximations have been proposed. The deterministic rate equation (DRE) gives a macroscopic approximation as a compact system of differential equations that estimate the average populations for each species, but it may be inaccurate in the case of nonlinear interaction dynamics. Here we propose finite-state expansion (FSE), an analytical method mediating between the microscopic and the macroscopic interpretations of a stochastic reaction network by coupling the master equation dynamics of a chosen subset of the discrete state space with the mean population dynamics of the DRE. An algorithm translates a network into ...
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Stochastic reaction networks are a fundamental model to describe interactions between species whe... more Stochastic reaction networks are a fundamental model to describe interactions between species where random fluctuations are relevant. The master equation provides the evolution of the probability distribution across the discrete state space consisting of vectors of population counts for each species. However, since its exact solution is often elusive, several analytical approximations have been proposed. The deterministic rate equation (DRE) gives a macroscopic approximation as a compact system of differential equations that estimate the average populations for each species, but it may be inaccurate in the case of nonlinear interaction dynamics. Here we propose finite-state expansion (FSE), an analytical method mediating between the microscopic and the macroscopic interpretations of a stochastic reaction network by coupling the master equation dynamics of a chosen subset of the discrete state space with the mean population dynamics of the DRE. An algorithm translates a network into ...
We propose a novel approach to the statistical analysis of simulation models and, especially, age... more We propose a novel approach to the statistical analysis of simulation models and, especially, agent-based models (ABMs). Our main goal is to provide a fully automated and model-independent tool-kit to inspect simulations and perform counter-factual analysis. Our approach: (i) is easy-to-use by the modeller, (ii) improves reproducibility of results, (iii) optimizes running time given the modeller’s machine, (iv) automatically chooses the number of required simulations and simulation steps to reach user-specified statistical confidence, and (v) automatically performs a variety of statistical tests. In particular, our framework is designed to distinguish the transient dynamics of the model from its steady state behaviour (if any), estimate properties of the model in both “phases”, and provide indications on the ergodic (or non-ergodic) nature of the simulated processes – which, in turns allows one to gauge the reliability of a steady state analysis. Estimates are equipped with statisti...
The problem of comparison and minimization for ordinary differential equations (ODEs) through beh... more The problem of comparison and minimization for ordinary differential equations (ODEs) through behavioral equivalences has been tackled so far using exact notions. However these may not be robust enough in practice because they are highly sensitive to the specific choice of parameters. We study ODEs with polynomial derivatives of any degree, covering linear/affine systems and chemical reaction networks with mass-action kinetics. For this class, we introduce approximate differential equivalence as a more permissive notion that allows variables of an ODE system to be related even if they vary in their parameters up to a given tolerance. We develop algorithms to (i) compute the largest approximate differential equivalence, (ii) construct a quotient approximate model from the original one via an appropriate perturbation of the parameters, and (iii) provide a formal certificate on the quality of the approximation. Finally, we apply approximate differential equivalences for symmetry reduct...
BPMN collaboration models have acquired increasing relevance in software development since they s... more BPMN collaboration models have acquired increasing relevance in software development since they shorten the communication gap between domain experts and IT specialists and permit clarifying the characteristics of software systems needed to provide automatic support for the activities of complex organisations. Nonetheless, the lack of effective formal verification capabilities can hinder the full adoption of the BPMN standard by IT specialists, as it prevents precisely check the satisfaction of behavioural properties, with negative impacts on the quality of the software. To address these issues, this paper proposes BProVe, a novel verification approach for BPMN collaborations. This combines both standard model checking techniques, through the MAUDE’s LTL model checker, and statistical model checking techniques, through the statistical analyser MULTIVESTA. The latter makes BProVe effective also on those scenarios suffering from the state-space explosion problem, made even more acute b...
The ASCENS project deals with designing systems as ensembles of adaptive components. Among the ou... more The ASCENS project deals with designing systems as ensembles of adaptive components. Among the outputs of the ASCENS project are multiple tools that address particular issues in designing the ensembles, ranging from support for early stage formal modeling to runtime environment for executing and monitoring ensemble implementations. The goal of this chapter is to provide a compact description of the individual tools, which is supplemented by additional downloadable material on the project website.
One of the most distinctive features of collective adaptive systems (CAS) is the presence of many... more One of the most distinctive features of collective adaptive systems (CAS) is the presence of many individuals which interact with each other and with the environment, giving rise to a system-level behaviour that cannot be analyzed by studying the single agents in isolation. The interaction structure among the individuals of CAS is often captured by networks where nodes denote individuals and edges interactions. Understanding the interplay between the network topology and the CAS dynamics calls for tools from network theory in order, for instance, to identify the most important nodes of a network. Centrality measures address this task by assigning an importance measure to each node, a possible example being the famous PageRank algorithm of Google. In this paper we investigate the relationship between centrality measures and model reduction techniques, such as lumpability of Markov chains, which seek to reduce a model into a smaller one that can be processed more efficiently, while pr...
CARMA (Collective Adaptive Resource-sharing Markovian Agents) is a process-algebra-based quantita... more CARMA (Collective Adaptive Resource-sharing Markovian Agents) is a process-algebra-based quantitative language developed for the modeling of collective adaptive systems. A CARMA model consists of an environment in which a collective of components with attribute stores interact via unicast and broadcast communication, providing a rich modeling formalism. The semantics of a CARMA model are given by a continuous-time Markov chain which can be simulated using the CARMA Eclipse Plug-in. Furthermore, statistical model checking can be applied to the trajectories generated through simulation using the MultiVeStA tool. This advanced tutorial will introduce some of the theory behind CARMA and MultiVeStA as well as demonstrate its application to collective adaptive system modeling.
Domain-specific quantitative modeling and analysis approaches are fundamental in scenarios in whi... more Domain-specific quantitative modeling and analysis approaches are fundamental in scenarios in which qualitative approaches are inappropriate or unfeasible. In this paper, we present a tool-supported approach to quantitative graph-based security risk modeling and analysis based on attack-defense trees. Our approach is based on QFLan , a successful domain-specific approach to support quantitative modeling and analysis of highly configurable systems, whose domain-specific components have been decoupled to facilitate the instantiation of the QFLan approach in the domain of graph-based security risk modeling and analysis. Our approach incorporates distinctive features from three popular kinds of attack trees, namely enhanced attack trees, capabilities-based attack trees and attack countermeasure trees, into the domain-specific modeling language. The result is a new framework, called RisQFLan , to support quantitative security risk modeling and analysis based on attack-defense diagrams. B...
We introduce polynomial couplings, a generalization of probabilistic couplings, to develop an alg... more We introduce polynomial couplings, a generalization of probabilistic couplings, to develop an algorithm for the computation of equivalence relations which can be interpreted as a lifting of probabilistic bisimulation to polynomial differential equations, a ubiquitous model of dynamical systems across science and engineering. The algorithm enjoys polynomial time complexity and complements classical partition-refinement approaches because: (a) it implements a local exploration of the system, possibly yielding equivalences that do not necessarily involve the inspection of the whole system of differential equations; (b) it can be enhanced by up-to techniques; and (c) it allows the specification of pairs which ought not be included in the output. Using a prototype, these advantages are demonstrated on case studies from systems biology for applications to model reduction and comparison. Notably, we report four orders of magnitude smaller runtimes than partition-refinement approaches when ...
This short paper summarises the contributions published in [4], where we introduce QFLan, a frame... more This short paper summarises the contributions published in [4], where we introduce QFLan, a framework for quantitative modeling and analysis of highly (re)configurable systems, like software product lines. We define a rich domain specific language (DSL) for systems with variability in terms of features, which can be dynamically installed, removed or replaced, capable of modeling probabilistic behavior, possibly subject to quantitative feature constraints. High-level DSL specifications are automatically encoded in a process algebra whose operational behavior interacts with a store of constraints, which allows to separate a system’s configuration from its behavior. The resulting probabilistic configurations and behavior converge seamlessly in a semantics based on discrete-time Markov chains, thus enabling quantitative analysis. An accompanying Eclipse-based tool offers a modern integrated development environment to specify such systems and to perform analyses that range from the likel...
Stochastic reaction networks are a fundamental model to describe interactions between species whe... more Stochastic reaction networks are a fundamental model to describe interactions between species where random fluctuations are relevant. The master equation provides the evolution of the probability distribution across the discrete state space consisting of vectors of population counts for each species. However, since its exact solution is often elusive, several analytical approximations have been proposed. The deterministic rate equation (DRE) gives a macroscopic approximation as a compact system of differential equations that estimate the average populations for each species, but it may be inaccurate in the case of nonlinear interaction dynamics. Here we propose finite-state expansion (FSE), an analytical method mediating between the microscopic and the macroscopic interpretations of a stochastic reaction network by coupling the master equation dynamics of a chosen subset of the discrete state space with the mean population dynamics of the DRE. An algorithm translates a network into ...
Uploads