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Stochastic Differential Dynamic Logic for Stochastic Hybrid Programs
, 2011
"... should not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution or government. A conference version of this report has appeared at CADE [Pla11].Keywords: Dynamic logic, proof calculus, stochastic differential equations, stochastic hybrid Lo ..."
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Cited by 19 (14 self)
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should not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution or government. A conference version of this report has appeared at CADE [Pla11].Keywords: Dynamic logic, proof calculus, stochastic differential equations, stochastic hybrid Logic is a powerful tool for analyzing and verifying systems, including programs, discrete systems, real-time systems, hybrid systems, and distributed systems. Some applications also have a stochastic behavior, however, either because of fundamental properties of nature, uncertain environments, or simplifications to overcome complexity. Discrete probabilistic systems have been studied using logic. But logic has been chronically underdeveloped in the context of stochastic hybrid systems, i.e., systems with interacting discrete, continuous, and stochastic dynamics. We aim at overcoming this deficiency and introduce a dynamic logic for stochastic hybrid systems. Our results indicate that logic is a promising tool for understanding stochastic hybrid systems and can help taming some of their complexity. We introduce a compositional model for stochastic hybrid systems. We prove adaptivity, càdlàg, and Markov time properties, and prove that the semantics
Logics of Dynamical Systems
"... We study the logic of dynamical systems, that is, logics and proof principles for properties of dynamical systems. Dynamical systems are mathematical models describing how the state of a system evolves over time. They are important in modeling and understanding many applications, including embedded ..."
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Cited by 18 (17 self)
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We study the logic of dynamical systems, that is, logics and proof principles for properties of dynamical systems. Dynamical systems are mathematical models describing how the state of a system evolves over time. They are important in modeling and understanding many applications, including embedded systems and cyber-physical systems. In discrete dynamical systems, the state evolves in discrete steps, one step at a time, as described by a difference equation or discrete state transition relation. In continuous dynamical systems, the state evolves continuously along a function, typically described by a differential equation. Hybrid dynamical systems or hybrid systems combine both discrete and continuous dynamics. Distributed hybrid systems combine distributed systems with hybrid systems, i.e., they are multi-agent hybrid systems that interact through remote communication or physical interaction. Stochastic hybrid systems combine stochastic
Statistical model checking for cyber-physical systems.
- In Tevfik Bultan and Pao-Ann Hsiung,
, 2011
"... Abstract. Statistical Model Checking is useful in situations where it is either inconvenient or impossible to build a concise representation of the global transition relation. This happens frequently with cyberphysical systems: Two examples are verifying Stateflow-Simulink models and in reasoning a ..."
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Cited by 17 (0 self)
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Abstract. Statistical Model Checking is useful in situations where it is either inconvenient or impossible to build a concise representation of the global transition relation. This happens frequently with cyberphysical systems: Two examples are verifying Stateflow-Simulink models and in reasoning about biochemical reactions in Systems Biology. The main problem with Statistical Model Checking is caused by rare events. We describe how Statistical Model Checking works and demonstrate the problem with rare events. We then describe how Importance Sampling with the Cross-Entropy Technique can be used to address this problem.
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 formu-lated 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 formu-lated 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. Ex-perimental results indicate that the local search procedure improves upon the results of pure stochastic optimization algorithms.
Querying parametric temporal logic properties on embedded systems
- In Int. Conference on Testing Software and Systems
, 2012
"... Abstract. In Model Based Development (MBD) of embedded systems, it is often desirable to not only verify/falsify certain formal system spec-ifications, but also to automatically explore the properties that the sys-tem satisfies. Namely, given a parametric specification, we would like to automaticall ..."
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Cited by 7 (5 self)
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Abstract. In Model Based Development (MBD) of embedded systems, it is often desirable to not only verify/falsify certain formal system spec-ifications, but also to automatically explore the properties that the sys-tem satisfies. Namely, given a parametric specification, we would like to automatically infer the ranges of parameters for which the property holds/does not hold on the system. In this paper, we consider parametric specifications in Metric Temporal Logic (MTL). Using robust semantics for MTL, the parameter estimation problem can be converted into an optimization problem which can be solved by utilizing stochastic opti-mization methods. The framework is demonstrated on some examples from the literature. 1
A COMPLETE AXIOMATIZATION OF QUANTIFIED DIFFERENTIAL DYNAMIC LOGIC FOR DISTRIBUTED HYBRID SYSTEMS
"... Abstract. We address a fundamental mismatch between the combinations of dynamics that occur in cyber-physical systems and the limited kinds of dynamics supported in analysis. Modern applications combine communication, computation, and control. They may even form dynamic distributed networks, where n ..."
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Cited by 7 (7 self)
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Abstract. We address a fundamental mismatch between the combinations of dynamics that occur in cyber-physical systems and the limited kinds of dynamics supported in analysis. Modern applications combine communication, computation, and control. They may even form dynamic distributed networks, where neither structure nor dimension stay the same while the system follows hybrid dynamics, i.e., mixed discrete and continuous dynamics. We provide the logical foundations for closing this analytic gap. We develop a formal model for distributed hybrid systems. It combines quantified differential equations with quantified assignments and dynamic dimensionality-changes. We introduce a dynamic logic for verifying distributed hybrid systems and present a proof calculus for this logic. This is the first formal verification approach for distributed hybrid systems. We prove that our calculus is a sound and complete axiomatization of the behavior of distributed hybrid systems relative to quantified differential equations. In our calculus we have proven collision freedom in distributed car control even when an unbounded number of new cars may appear dynamically on the road. 1.
Fainekos. Simulating Insulin Infusion Pump Risks by In-Silico Modeling
- of the Insulin-Glucose Regulatory System. CMSB
, 2012
"... Abstract. We present a case-study on the use of robustness-guided and statistical model checking approaches for simulating risks due to insulin infusion pump usage by diabetic patients. Insulin infusion pumps allow for a continuous delivery of insulin with varying rates and delivery profiles to help ..."
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Cited by 7 (2 self)
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Abstract. We present a case-study on the use of robustness-guided and statistical model checking approaches for simulating risks due to insulin infusion pump usage by diabetic patients. Insulin infusion pumps allow for a continuous delivery of insulin with varying rates and delivery profiles to help patients self-regulate their blood glucose levels. However, the use of infusion pumps and continuous glucose monitors can pose risks to the patient including chronically elevated blood glucose levels (hyperglycemia) or dangerously low glucose levels (hypoglycemia). In this paper, we use mathematical models of the basic insulin-glucose regulatory system in a diabetic patient, insulin infusion pumps, and the user’s interaction with these pumps defined by commonly used insulin infusion strategies for maintaining normal glucose levels. These strategies include common guidelines taught to patients by physicians and certified diabetes educators and have been implemented in commercially available insulin bolus calculators. Furthermore, we model the failures in the devices themselves along with common errors in the usage of the pump. We compose these models together and analyze them using two related techniques: (a) robustness guided state-space search to explore worstcase scenarios and (b) statistical model checking techniques to assess the probabilities of hyper- and hypoglycemia risks. Our technique can be used to identify the worst-case effects of the combination of many different kinds of failures and place high confidence bounds on their probabilities. 1
Monitor-Based Statistical Model Checking for Weighted Metric Temporal Logic
, 2012
"... Abstract. We present a novel approach and implementation for analysing weighted timed automata (WTA) with respect to the weighted metric temporal logic (WMTL≤). Based on a stochastic semantics of WTAs, we apply statistical model checking (SMC) to estimate and test probabilities of satisfaction with ..."
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Abstract. We present a novel approach and implementation for analysing weighted timed automata (WTA) with respect to the weighted metric temporal logic (WMTL≤). Based on a stochastic semantics of WTAs, we apply statistical model checking (SMC) to estimate and test probabilities of satisfaction with desired levels of confidence. Our approach consists in generation of deterministic monitors for formulas in WMTL≤, allowing for efficient SMC by run-time evaluation of a given formula. By necessity, the deterministic observers are in general approximate (over- or under-approximations), but are most often exact and experimentally tight. The technique is implemented in the new tool Casaal that we seamlessly connect to Uppaal-smc in a tool chain. We demonstrate the applicability of our technique and the efficiency of our implementation through a number of case-studies. 1
System Level Formal Verification via Model Checking Driven Simulation
"... Abstract. We show how by combining Explicit Model Checking techniques and simulation it is possible to effectively carry out (bounded) System Level Formal Verification of large Hybrid Systems such as those defined using model-based tools like Simulink. We use an explicit model checker (namely, CMurp ..."
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Cited by 6 (4 self)
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Abstract. We show how by combining Explicit Model Checking techniques and simulation it is possible to effectively carry out (bounded) System Level Formal Verification of large Hybrid Systems such as those defined using model-based tools like Simulink. We use an explicit model checker (namely, CMurphi) to generate all possible (finite horizon) simulation scenarios and then optimise the simulation of such scenarios by exploiting the ability of simulators to save and restore visited states. We show feasibility of our approach by presenting experimental results on the verification of the fuel control system example in the Simulink distribution. To the best of our knowledge this is the first time that (exhaustive) verification has been carried out for hybrid systems of such a size. 1
Statistical Model Checking QoS Properties of Systems with SBIP
- In Leveraging Applications of Formal Methods, Verification and Validation. Technologies for Mastering Change, volume 7609 of LNCS
, 2012
"... HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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Cited by 4 (4 self)
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HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
