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12
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 43 (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.
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 21 (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
Breach: A Toolbox for Verification and Parameter Synthesis of Hybrid Systems
 In ComputerAided Verification
, 2010
"... Abstract. We describe Breach, a Matlab toolbox providing a coherent set of simulationbased techniques aimed at the analysis of deterministic models of hybrid dynamical systems. The primary feature of Breach is to facilitate the computation and the property investigation of large sets of trajectorie ..."
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Cited by 20 (2 self)
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Abstract. We describe Breach, a Matlab toolbox providing a coherent set of simulationbased techniques aimed at the analysis of deterministic models of hybrid dynamical systems. The primary feature of Breach is to facilitate the computation and the property investigation of large sets of trajectories. It relies on an efficient numerical solver of ordinary differential equations that can also provide information about sensitivity with respect to parameters variation. The latter is used to perform approximate reachability analysis and parameter synthesis. A major novel feature is the robust monitoring of metric interval temporal logic (MITL) formulas. The application domain of Breach ranges from embedded systems design using Simulink to the analysis of complex nonlinear models from systems biology. 1
Parameter Synthesis in Nonlinear Dynamical Systems: Application to Systems Biology
"... Abstract. The dynamics of biological processes are often modeled as systems of nonlinear ordinary differential equations (ODE). An important feature of nonlinear ODEs is that seemingly minor changes in initial conditions or parameters can lead to radically different behaviors. This is problematic be ..."
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Cited by 13 (0 self)
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Abstract. The dynamics of biological processes are often modeled as systems of nonlinear ordinary differential equations (ODE). An important feature of nonlinear ODEs is that seemingly minor changes in initial conditions or parameters can lead to radically different behaviors. This is problematic because in general it is never possible to know/measure the precise state of any biological system due to measurement errors. The parameter synthesis problem is to identify sets of parameters (including initial conditions) for which a given system of nonlinear ODEs does not reach a given set of undesirable states. We present an efficient algorithm for solving this problem that combines sensitivity analysis with an efficient search over initial conditions. It scales to highdimensional models and is exact if the given model is affine. We demonstrate our method on a model of the acute inflammatory response to bacterial infection, and identify initial conditions consistent with 3 biologically relevant outcomes.
Automated Verification of DenseTime MTL Specifications via DiscreteTime Approximation ⋆
"... Abstract. This paper presents a verification technique for densetime MTL based on discretization. The technique reduces the validity problem of MTL formulas from dense to discrete time, through the notion of sampling invariance, introduced in previous work [13]. Since the reduction is from an undec ..."
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Cited by 5 (5 self)
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Abstract. This paper presents a verification technique for densetime MTL based on discretization. The technique reduces the validity problem of MTL formulas from dense to discrete time, through the notion of sampling invariance, introduced in previous work [13]. Since the reduction is from an undecidable problem to a decidable one, the technique is necessarily incomplete, so it fails to provide conclusive answers for some formulas. The paper discusses this shortcoming and hints at how it can be mitigated in practice. The verification technique has been implemented on top of the�ot tool [19] for discretetime bounded validity checking; the paper also reports on inthesmall experiments with the tool, which show some results that are promising in terms of performance.
Practical automated partial verification of multiparadigm realtime models
 In Proc. of ICFEM’08, volume 5256/1 of LNCS
, 2008
"... This article introduces a fully automated verification technique that permits to analyze realtime systems described using a continuous notion of time and a mixture of operational (i.e., automatabased) and descriptive (i.e., logicbased) formalisms. The technique relies on the reduction, under reas ..."
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This article introduces a fully automated verification technique that permits to analyze realtime systems described using a continuous notion of time and a mixture of operational (i.e., automatabased) and descriptive (i.e., logicbased) formalisms. The technique relies on the reduction, under reasonable assumptions, of the continuoustime verification problem to its discretetime counterpart. This reconciles in a viable and effective way the dense/discrete and operational/descriptive dichotomies that are often encountered in practice when it comes to specifying and analyzing complex critical systems. The article investigates the applicability of the technique through a significant example centered on a communication protocol. More precisely, concurrent runs of the protocol are formalized by parallel instances of a Timed Automaton, while the synchronization rules between these instances are specified through Metric Temporal Logic formulas, thus creating a multiparadigm model. Verification tests run on
A Formal Methods Approach to Pattern Synthesis in Reaction Diffusion Systems
"... Abstract — We propose a technique to detect and generate patterns in a network of locally interacting dynamical systems. Central to our approach is a novel spatial superposition logic, whose semantics is defined over the quadtree of a partitioned image. We show that formulas in this logic can be ef ..."
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Cited by 1 (1 self)
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Abstract — We propose a technique to detect and generate patterns in a network of locally interacting dynamical systems. Central to our approach is a novel spatial superposition logic, whose semantics is defined over the quadtree of a partitioned image. We show that formulas in this logic can be efficiently learned from positive and negative examples of several types of patterns. We also demonstrate that pattern detection, which is implemented as a model checking algorithm, performs very well for test data sets different from the learning sets. We define a quantitative semantics for the logic and integrate the model checking algorithm with particle swarm optimization in a computational framework for synthesis of parameters leading to desired patterns in reactiondiffusion systems. I.
Application to Systems Biology
"... Abstract. The dynamics of biological processes are often modeled as systems of nonlinear ordinary differential equations (ODE). An important feature of nonlinear ODEs is that seemingly minor changes in initial conditions or parameters can lead to radically different behaviors. This is problematic be ..."
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Abstract. The dynamics of biological processes are often modeled as systems of nonlinear ordinary differential equations (ODE). An important feature of nonlinear ODEs is that seemingly minor changes in initial conditions or parameters can lead to radically different behaviors. This is problematic because in general it is never possible to know/measure the precise state of any biological system due to measurement errors. The parameter synthesis problem is to identify sets of parameters (including initial conditions) for which a given system of nonlinear ODEs does not reach a given set of undesirable states. We present an efficient algorithm for solving this problem that combines sensitivity analysis with an efficient search over initial conditions. It scales to highdimensional models and is exact if the given model is affine. We demonstrate our method on a model of the acute inflammatory response
Dynamic Programming algorithm for Computing Temporal Logic Robustness
, 2013
"... i In this thesis we deal with the problem of temporal logic robustness estimation. We present a dynamic programming algorithm for the robust estimation problem of Metric Temporal Logic (MTL) formulas regarding a finite trace of time stated sequence. This algorithm not only tests if the MTL specifica ..."
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i In this thesis we deal with the problem of temporal logic robustness estimation. We present a dynamic programming algorithm for the robust estimation problem of Metric Temporal Logic (MTL) formulas regarding a finite trace of time stated sequence. This algorithm not only tests if the MTL specification is satisfied by the given input which is a finite system trajectory, but also quantifies to what extend does the sequence satisfies or violates the MTL specification. The implementation of the algorithm is the DPTALIRO toolbox for MATLAB. Currently it is used as the temporal logic robust computing engine of STALIRO which is a tool for MATLAB searching for trajectories of minimal robustness in Simulink / Stateflow. DPTALIRO is expected to have near linear running time and constant memory requirement depending on the structure of the MTL formula. DPTALIRO toolbox also integrates new features not supported in its ancestor FWTALIRO such as parameter replacement, most related iteration and most related predicate. A derivative of DPTALIRO which is DPTTALIRO is also addressed in this thesis which applies dynamic programming algorithm for time robustness computation. We test the running time of DPTALIRO and compare it with FWTALIRO. Finally, we present an application where DPTALIRO is used as the robustness computation core of STALIRO for a parameter estimation problem. ii ACKNOWLEDGEMENTS I want to thank Dr. Georgios Fainekos for this wonderful opportunity to work on this interesting research topic and more importantly work along with him. I benefit greatly from his guidance, rigorous attitude and forwardlooking spirit. I appreciate the financial support from Dr. Georgios Fainekos and Arizona State University in the past two years. I would also like to thank Dr. Hessam Sarjoughian and Dr. Aviral.Shrivastava for the
ETH Zurich
"... This paper revisits the classical notion of sampling in the setting of realtime temporal logics for the modeling and analysis of systems. The relationship between the satisfiability of Metric Temporal Logic (MTL) formulas over continuoustime models and over discretetime models is studied. It is s ..."
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This paper revisits the classical notion of sampling in the setting of realtime temporal logics for the modeling and analysis of systems. The relationship between the satisfiability of Metric Temporal Logic (MTL) formulas over continuoustime models and over discretetime models is studied. It is shown to what extent discretetime sequences obtained by sampling continuoustime signals capture the semantics of MTL formulas over the two time domains. The main results apply to “flat ” formulas that do not nest temporal operators and can be applied to the problem of reducing the verification problem for MTL over continuoustime models to the same problem over discretetime, resulting in an automated partial practicallyefficient discretization technique.