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37
Robustness of Temporal Logic Specifications for ContinuousTime Signals
, 2009
"... In this paper, we consider the robust interpretation of Metric Temporal Logic (MTL) formulas over signals that take values in metric spaces. For such signals, which are generated by systems whose states are equipped with nontrivial metrics, for example continuous or hybrid, robustness is not only na ..."
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Cited by 42 (18 self)
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In this paper, we consider the robust interpretation of Metric Temporal Logic (MTL) formulas over signals that take values in metric spaces. For such signals, which are generated by systems whose states are equipped with nontrivial metrics, for example continuous or hybrid, robustness is not only natural, but also a critical measure of system performance. Thus, we propose multivalued semantics for MTL formulas, which capture not only the usual Boolean satisfiability of the formula, but also topological information regarding the distance, ε, from unsatisfiability. We prove that any other signal that remains εclose to the initial one also satisfies the same MTL specification under the usual Boolean semantics. Finally, our framework is applied to the problem of testing formulas of two fragments of MTL, namely Metric Interval Temporal Logic (MITL) and closed Metric Temporal Logic (clMTL), over continuoustime signals using only discretetime analysis. The motivating idea behind our approach is that if the continuoustime signal fulfills certain conditions and the discrete time signal robustly satisfies the temporal logic specification, then the corresponding continuoustime signal should also satisfy the same temporal logic specification.
STaLiRo: A Tool for Temporal Logic Falsification for Hybrid Systems ⋆
"... Abstract. STaLiRo is a Matlab (TM) toolbox that searches for trajectories of minimal robustness in Simulink/Stateflow diagrams. It can analyze arbitrary Simulink models or user defined functions that model the system. At the heart of the tool, we use randomized testing based on stochastic optimizat ..."
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Cited by 34 (19 self)
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Abstract. STaLiRo is a Matlab (TM) toolbox that searches for trajectories of minimal robustness in Simulink/Stateflow diagrams. It can analyze arbitrary Simulink models or user defined functions that model the system. At the heart of the tool, we use randomized testing based on stochastic optimization techniques including MonteCarlo methods and AntColony Optimization. Among the advantages of the toolbox is the seamless integration inside the Matlab environment, which is widely used in the industry for modelbased development of control software. We present the architecture of STaLiRo and its working on an application example. 1
Robust Satisfaction of Temporal Logic over RealValued Signals
"... Abstract. We consider temporal logic formulae specifying constraints in continuous time and space on the behaviors of continuous and hybrid dynamical system admitting uncertain parameters. We present several variants of robustness measures that indicate how far a given trajectory stands, in space an ..."
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Cited by 31 (7 self)
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Abstract. We consider temporal logic formulae specifying constraints in continuous time and space on the behaviors of continuous and hybrid dynamical system admitting uncertain parameters. We present several variants of robustness measures that indicate how far a given trajectory stands, in space and time, from satisfying or violating a property. We present a method to compute these robustness measures as well as their sensitivity to the parameters of the system or parameters appearing in the formula. Combined with an appropriate strategy for exploring the parameter space, this technique can be used to guide simulationbased verification of complex nonlinear and hybrid systems against temporal properties. Our methodology can be used for other nontraditional applications of temporal logic such as characterizing subsets of the parameter space for which a system is guaranteed to satisfy a formula with a desired robustness degree. 1
A general computational method for robustness analysis with applications to synthetic gene networks
, 2009
"... Motivation: Robustness is the capacity of a system to maintain a function in the face of perturbations. It is essential for the correct functioning of natural and engineered biological systems. Robustness is generally defined in an adhoc, problemdependent manner, thus hampering the fruitful develo ..."
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Cited by 22 (7 self)
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Motivation: Robustness is the capacity of a system to maintain a function in the face of perturbations. It is essential for the correct functioning of natural and engineered biological systems. Robustness is generally defined in an adhoc, problemdependent manner, thus hampering the fruitful development of a theory of biological robustness, advocated by Kitano [Mol Syst Biol, 3:137, 2007]. Results: In this paper, we propose a general definition of robustness that applies to any biological function expressible in temporal logic LTL, and to broad model classes and perturbation types. Moreover, we propose a computational approach and an implementation in BIOCHAM 2.8 for the automated estimation of the robustness of a given behavior with respect to a given set of perturbations. The applicability and biological relevance of our approach is demonstrated by testing and improving the robustness of the timed behavior of a synthetic transcriptional cascade that could be used as a biological timer for synthetic biology applications. Availability: Version 2.8 of BIOCHAM and the transcriptional cascade model are available at
H.: Verification of automotive control applications using staliro
 In: Proceedings of the American Control Conference (2012
"... Abstract — STALIRO is a software toolbox that performs stochastic search for system trajectories that falsify realtime temporal logic specifications. STALIRO is founded on the notion of robustness of temporal logic specifications. In this paper, we present a dynamic programming algorithm for compu ..."
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Cited by 17 (10 self)
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Abstract — STALIRO is a software toolbox that performs stochastic search for system trajectories that falsify realtime temporal logic specifications. STALIRO is founded on the notion of robustness of temporal logic specifications. In this paper, we present a dynamic programming algorithm for computing the robustness of temporal logic specifications with respect to system trajectories. We also demonstrate that typical automotive functional requirements can be captured and falsified using temporal logics and STALIRO. I.
Probabilistic Temporal Logic Falsification of CyberPhysical Systems
"... We present a MonteCarlo optimization technique for finding system behaviors that falsify a Metric Temporal Logic (MTL) property. Our approach performs a random walk over the space of system inputs guided by a robustness metric defined by the MTL property. Robustness is guiding the search for a fals ..."
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Cited by 14 (12 self)
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We present a MonteCarlo optimization technique for finding system behaviors that falsify a Metric Temporal Logic (MTL) property. Our approach performs a random walk over the space of system inputs guided by a robustness metric defined by the MTL property. Robustness is guiding the search for a falsifying behavior by exploring trajectories with smaller robustness values. The resulting testing framework can be applied to a wide class of CyberPhysical Systems (CPS). We show through experiments on complex system models that using our framework can help automatically falsify properties with more consistency as compared to other means such as uniform sampling.
Fainekos, “Falsification of temporal properties of hybrid systems using the crossentropy method
 in HSCC. ACM
"... Randomized testing is a popular approach for checking properties of large embedded system designs. It is well known that a uniform random choice of test inputs is often suboptimal. Ideally, the choice of inputs has to be guided by choosing the right input distributions in order to expose cornercas ..."
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Cited by 12 (5 self)
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Randomized testing is a popular approach for checking properties of large embedded system designs. It is well known that a uniform random choice of test inputs is often suboptimal. Ideally, the choice of inputs has to be guided by choosing the right input distributions in order to expose cornercase violations. However, this is also known to be a hard problem, in practice. In this paper, we present an application of the crossentropy method for adaptively choosing input distributions for falsifying temporal logic properties of hybrid systems. We present various choices for representing input distribution families for the crossentropy method, ranging from a complete partitioning of the input space into cells to a factored distribution of the input using graphical models. Finally, we experimentally compare the falsification approach using the crossentropy method to other stochastic and heuristic optimization techniques implemented inside the tool STaliro over a set of benchmark systems. The performance of the cross entropy method is quite promising. We find that sampling inputs using the crossentropy method guided by trace robustness can discover violations faster, and more consistently than the other competing methods considered.
O.: Refining dynamics of gene regulatory networks in a stochastic πcalculus framework
 In: Transactions on Computational Systems Biology XIII
, 2011
"... Abstract. In this paper, we introduce a framework allowing to model and analyse efficiently Gene Regulatory Networks in their temporal and stochastic aspects. The analysis of stable states and inference of René Thomas ’ discrete parameters derives from this logical formalism. We offer a compositiona ..."
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Cited by 12 (9 self)
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Abstract. In this paper, we introduce a framework allowing to model and analyse efficiently Gene Regulatory Networks in their temporal and stochastic aspects. The analysis of stable states and inference of René Thomas ’ discrete parameters derives from this logical formalism. We offer a compositional approach which comes with a natural translation to the Stochastic πCalculus. The method we propose consists in successive refinements of generalized dynamics of Gene Regulatory Networks. We apply this method to the control of the differentiation in a Gene Regulatory Network generalizing metazoan segmentation processes. 1
Parametric Identification of Temporal Properties
"... Abstract. Given a densetime realvalued signal and a parameterized temporal logic formula with both magnitude and timing parameters, we compute the subset of the parameter space that renders the formula satisfied by the trace. We provide two preliminary implementations, one which follows the exact ..."
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Cited by 9 (2 self)
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Abstract. Given a densetime realvalued signal and a parameterized temporal logic formula with both magnitude and timing parameters, we compute the subset of the parameter space that renders the formula satisfied by the trace. We provide two preliminary implementations, one which follows the exact semantics and attempts to compute the validity domain by quantifier elimination in linear arithmetics and one which conducts adaptive search in the parameter space. 1
Linear hybrid system falsification through descent
"... Abstract. In this paper, we address the problem of local search for the falsification of hybrid automata with affine dynamics. Namely, given a sequence of locations and a maximum simulation time, we return the trajectory that comes closest to the unsafe set. This problem is formulated as a differen ..."
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Cited by 7 (5 self)
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Abstract. In this paper, we address the problem of local search for the falsification of hybrid automata with affine dynamics. Namely, given a sequence of locations and a maximum simulation time, we return the trajectory that comes closest to the unsafe set. This problem is formulated as a differentiable optimization problem and solved. The purpose of developing such a local search method is to combine it with high level stochastic optimization algorithms in order to falsify hybrid systems with complex discrete dynamics and high dimensional continuous spaces. Experimental results indicate that the local search procedure improves upon the results of pure stochastic optimization algorithms.