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Synthesis for PCTL in parametric Markov decision processes.
 In NASA Formal Methods (NFM),
, 2011
"... Abstract. In parametric Markov Decision Processes (PMDPs), transition probabilities are not fixed, but are given as functions over a set of parameters. A PMDP denotes a family of concrete MDPs. This paper studies the synthesis problem for PCTL in PMDPs: Given a specification Φ in PCTL, we synthesis ..."
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Abstract. In parametric Markov Decision Processes (PMDPs), transition probabilities are not fixed, but are given as functions over a set of parameters. A PMDP denotes a family of concrete MDPs. This paper studies the synthesis problem for PCTL in PMDPs: Given a specification Φ in PCTL, we synthesise the parameter valuations under which Φ is true. First, we divide the possible parameter space into hyperrectangles. We use existing decision procedures to check whether Φ holds on each of the Markov processes represented by the hyperrectangle. As it is normally impossible to cover the whole parameter space by hyperrectangles, we allow a limited area to remain undecided. We also consider an extension of PCTL with reachability rewards. To demonstrate the applicability of the approach, we apply our technique on a case study, using a preliminary implementation.
δComplete Analysis for Bounded Reachability of Hybrid Systems
, 2014
"... We present the framework of δcomplete analysis for bounded reachability problems of general hybrid systems. We perform bounded reachability checking through solving δdecision problems over the reals. The techniques take into account of robustness properties of the systems under numerical perturbat ..."
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We present the framework of δcomplete analysis for bounded reachability problems of general hybrid systems. We perform bounded reachability checking through solving δdecision problems over the reals. The techniques take into account of robustness properties of the systems under numerical perturbations. We prove that the verification problems become much more mathematically tractable in this new framework. Our implementation of the techniques, an opensource tool dReach, scales well on several highly nonlinear hybrid system models that arise in biomedical and robotics applications.
Abstraction of Elementary Hybrid Systems by Variable Transformation
"... Elementary hybrid systems (EHSs) are those hybrid systems (HSs) containing elementary functions such as exp, ln, sin, cos, etc. EHSs are very common in practice, especially in safetycritical domains. Due to the nonpolynomial expressions which lead to undecidable arithmetic, verification of EHSs i ..."
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Elementary hybrid systems (EHSs) are those hybrid systems (HSs) containing elementary functions such as exp, ln, sin, cos, etc. EHSs are very common in practice, especially in safetycritical domains. Due to the nonpolynomial expressions which lead to undecidable arithmetic, verification of EHSs is very hard. Existing approaches based on partition of the state space or overapproximation of reachable sets suffer from state space explosion or inflation of numerical errors. In this paper, we propose a symbolic abstraction approach that reduces EHSs to polynomial hybrid systems (PHSs), by replacing all nonpolynomial terms with newly introduced variables. Thus the verification of EHSs is reduced to the one of PHSs, enabling us to apply all the wellestablished verification techniques and tools for PHSs to EHSs. In this way, it is possible to avoid the limitations of many existing methods. We illustrate the abstraction approach and its application in safety verification of EHSs by several real world examples.
Creative Commons Attribution License. Approximated Symbolic Computations over Hybrid Automata∗
"... Hybrid automata are a natural framework for modeling and analyzing systems which exhibit a mixed discrete continuous behaviour. However, the standard operational semantics defined over such models implicitly assume perfect knowledge of the real systems and infinite precision measurements. Such assu ..."
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Hybrid automata are a natural framework for modeling and analyzing systems which exhibit a mixed discrete continuous behaviour. However, the standard operational semantics defined over such models implicitly assume perfect knowledge of the real systems and infinite precision measurements. Such assumptions are not only unrealistic, but often lead to the construction of misleading models. For these reasons we believe that it is necessary to introduce more flexible semantics able to manage with noise, partial information, and finite precision instruments. In particular, in this paper we integrate in a single framework based on approximated semantics different over and underapproximation techniques for hybrid automata. Our framework allows to both compare, mix, and generalize such techniques obtaining different approximated reachability algorithms. 1
Dynamic Network Functional Comparison via Approximatebisimulation by
"... Abstract: It is generally unknown how to formally determine whether different neural networks have a similar behaviour. This question intimately relates to the problem of finding a suitable similarity measure to identify bounds on the inputoutput response distances of neural networks, which has s ..."
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Abstract: It is generally unknown how to formally determine whether different neural networks have a similar behaviour. This question intimately relates to the problem of finding a suitable similarity measure to identify bounds on the inputoutput response distances of neural networks, which has several interesting theoretical and computational implications. For example, it can allow one to speed up the learning processes by restricting the network parameter space, or to test the robustness of a network with respect to parameter variation. In this paper we develop a procedure that allows to compare neural structures among them. In particular, we consider dynamic networks composed of neural units characterised by nonlinear differential equations, described in terms of autonomous continuous dynamic systems. The comparison is established by importing and adapting from the formal verification setting the concept of δ−approximate bisimulations techniques for nonlinear systems. We have positively tested the proposed approach over continuous time recurrent neural networks (CTRNNs).
How to Capture Hybrid Systems Evolution Into Slices of Parallel Hyperplanes
"... Abstract: In this paper we make a step towards an algorithm for the verification of hybrid systems that, on the one hand allows very general inputs (e.g., with nonlinear ordinary differential equations), but on the other hand exploits the structure of those parts of the input that represent special ..."
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Abstract: In this paper we make a step towards an algorithm for the verification of hybrid systems that, on the one hand allows very general inputs (e.g., with nonlinear ordinary differential equations), but on the other hand exploits the structure of those parts of the input that represent special cases (e.g., clocks). We show how to compute slices of parallel hyperplanes separating reachable from unreachable parts of the state space for a given abstraction of the input system, and demonstrate the usefulness of such slices within an abstraction refinement algorithm based on hyperrectangles.