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Multi-Objective Parameter Synthesis in Probabilistic Hybrid Systems
"... Abstract. Technical systems interacting with the real world can be elegantly modelled using probabilistic hybrid automata (PHA). Parametric probabilistic hybrid automata are dynamical systems featuring hybrid discrete-continuous dynamics and parametric probabilistic branching, thereby generalizing ..."
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Abstract. Technical systems interacting with the real world can be elegantly modelled using probabilistic hybrid automata (PHA). Parametric probabilistic hybrid automata are dynamical systems featuring hybrid discrete-continuous dynamics and parametric probabilistic branching, thereby generalizing PHA by capturing a family of PHA within a single model. Such systems have a broad range of applications, from control systems over network protocols to biological components. We present a novel method to synthesize parameter instances (if such exist) of PHA satisfying a multi-objective bounded horizon specification over expected rewards. Our approach combines three techniques: statistical model checking of model instantiations, a symbolic version of importance sampling to handle the parametric dependence, and SAT-modulo-theory solving for finding feasible parameter instances in a multi-objective setting. The method provides statistical guarantees on the synthesized parameter instances. To illustrate the practical feasibility of the approach, we present experiments showing the potential benefit of the scheme compared to a naive parameter exploration approach.
Parameter Synthesis Through Temporal Logic Specifications?
"... Abstract. Parameters are often used to tune mathematical models and capture nondeterminism and uncertainty in physical and engineering systems. This paper is concerned with parametric nonlinear dynamical systems and the problem of determining the parameter values that are consistent with some expect ..."
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Abstract. Parameters are often used to tune mathematical models and capture nondeterminism and uncertainty in physical and engineering systems. This paper is concerned with parametric nonlinear dynamical systems and the problem of determining the parameter values that are consistent with some expected properties. In our previous works, we pro-posed a parameter synthesis algorithm limited to safety properties and demonstrated its applications for biological systems. Here we consider more general properties specified by a fragment of STL (Signal Tempo-ral Logic), which allows us to deal with complex behavioral patterns that biological processes exhibit. We propose an algorithm for parameter syn-thesis w.r.t. a property specified using the considered logic. It exploits reachable set computations and forward refinements. We instantiate our algorithm in the case of polynomial dynamical systems exploiting Bern-stein coefficients and we illustrate it on an epidemic model.
On Quantitative Modelling and Verification of DNA Walker Circuits Using Stochastic Petri Nets
"... Abstract. Molecular programming is an emerging field concerned with building synthetic biomolecular computing devices at the nanoscale, for example from DNA or RNA molecules. Many promising applications have been proposed, ranging from diagnostic biosensors and nanorobots to synthetic biology, but p ..."
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Abstract. Molecular programming is an emerging field concerned with building synthetic biomolecular computing devices at the nanoscale, for example from DNA or RNA molecules. Many promising applications have been proposed, ranging from diagnostic biosensors and nanorobots to synthetic biology, but prohibitive complexity and imprecision of ex-perimental observations makes reliability of molecular programs difficult to achieve. This paper advocates the development of design automation methodologies for molecular programming, highlighting the role of quan-titative verification in this context. We focus on DNA ‘walker ’ circuits, in which molecules can be programmed to traverse tracks placed on a DNA origami tile, taking appropriate decisions at junctions and reporting the outcome when reaching the end of the track. The behaviour of molecular walkers is inherently probabilistic and thus probabilistic model check-ing methods are needed for their analysis. We demonstrate how DNA walkers can be modelled using stochastic Petri nets, and apply statisti-cal model checking using the tool Cosmos to analyse the reliability and performance characteristics of the designs. The results are compared and contrasted with those obtained for the PRISM model checker. The paper ends by summarising future research challenges in the field. 1
