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14
Quantified Differential Dynamic Logic for Distributed Hybrid Systems
, 2010
"... We address a fundamental mismatch between the combinations of dynamics that occur in complex physical systems and the limited kinds of dynamics supported in analysis. Modern applications combine communication, computation, and control. They may even form dynamic networks, where neither structure nor ..."
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Cited by 21 (15 self)
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We address a fundamental mismatch between the combinations of dynamics that occur in complex physical systems and the limited kinds of dynamics supported in analysis. Modern applications combine communication, computation, and control. They may even form dynamic networks, where neither structure nor dimension stay the same while the system follows mixed discrete and continuous dynamics. We provide the logical foundations for closing this analytic gap. We develop a system model for distributed hybrid systems that 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 it. We prove that this 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 new cars may appear dynamically on the road.
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 18 (13 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 15 (15 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
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 8 (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.
Distributed Theorem Proving for Distributed Hybrid Systems ⋆
"... Abstract. Distributed hybrid systems present extraordinarily challenging problems for verification. On top of the notorious difficulties associated with distributed systems, they also exhibit continuous dynamics described by quantified differential equations. All serious proofs rely on decision proc ..."
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Cited by 8 (5 self)
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Abstract. Distributed hybrid systems present extraordinarily challenging problems for verification. On top of the notorious difficulties associated with distributed systems, they also exhibit continuous dynamics described by quantified differential equations. All serious proofs rely on decision procedures for real arithmetic, which can be extremely expensive. Quantified Differential Dynamic Logic (QdL) has been identified as a promising approach for getting a handle in this domain. QdL has been proved to be complete relative to quantified differential equations. But important questions remain as to how best to translate this theoretical result into practice: how do we succinctly specify a proof search strategy, and how do we control the computational cost? We address the problem of automated theorem proving for distributed hybrid systems. We identify a simple mode of use of QdL that cuts down on the enormous number of choices that it otherwise allows during proof search. We have designed a powerful strategy and tactics language for directing proof search. With these techniques, we have implemented a new automated theorem prover called KeYmaeraD. To overcome the high computational complexity of distributed hybrid systems verification, KeYmaeraD uses a distributed proving backend. We have experimentally observed that calls to the real arithmetic decision procedure can effectively be made in parallel. In this paper, we demonstrate these findings through an extended case study where we prove absence of collisions in a distributed car control system with a varying number of arbitrarily many cars. 1
Modelling and analyzing adaptive self-assembling strategies with Maude ⋆
"... Abstract. Building adaptive systems with predictable emergent behavior is a challenging task and is becoming a critical need. The research community has accepted the challenge by proposing approaches of various nature: from software architectures, to programming paradigms, to analysis techniques. Ou ..."
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Cited by 4 (0 self)
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Abstract. Building adaptive systems with predictable emergent behavior is a challenging task and is becoming a critical need. The research community has accepted the challenge by proposing approaches of various nature: from software architectures, to programming paradigms, to analysis techniques. Our own contribution in this regard is a conceptual framework for adaptation centered around the stressed role of control data. The framework is naturally realized in a reflective logical language like Maude by using the Reflective Russian Dolls model, as we show in this paper. We exploit the recently released statistical model checker PVesta to analyze a prominent example of adaptive system: robot swarms equipped with obstacle-avoidance self-assembly strategies.
Statistical Model Checking for Distributed Probabilistic-Control Hybrid Automata with Smart Grid Applications
, 2011
"... This technical report is a more detailed version of a published paper [12]. The power industry is currently moving towards a more dynamical, intelligent power grid. This Smart Grid is still in its infancy and a formal evaluation of the expensive technologies and ideas on the table is necessary befor ..."
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Cited by 3 (0 self)
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This technical report is a more detailed version of a published paper [12]. The power industry is currently moving towards a more dynamical, intelligent power grid. This Smart Grid is still in its infancy and a formal evaluation of the expensive technologies and ideas on the table is necessary before committing to a full investment. In this paper, we argue that a good model for the Smart Grid must match its basic properties: it must be hybrid (both evolve over time, and perform control/computation), distributed (multiple concurrently executing entities), and allow for asynchronous communication and stochastic behaviour (to accurately model real-world power consumption). We propose Distributed Probabilistic-Control Hybrid Automata (DPCHA) as a model for this purpose, and extend Bounded LTL to Quantified Bounded LTL in order to adapt and apply existing statistical model-checking techniques. We provide an implementation of a framework for developing and verifying DPCHAs. Finally, we conduct a case study for Smart Grid communications analysis. Keywords: statistical model checking, hybrid automata, hybrid systems, power
A Dynamic 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 for modeling and understanding many applications, including embedded ..."
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Cited by 1 (1 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 for 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 dynamics with hybrid systems. We survey dynamic logics for specifying and verifying properties for each of those classes of dynamical systems. A dynamic logic is a first-order modal logic with a pair of parametrized modal operators for each dynamical system to express necessary or possible properties of their transition behavior. Due to their full basis of first-order modal logic operators, dynamic logics can express a rich variety of system properties, including safety, controllability, reactivity, liveness, and quantified parametrized properties, even about
A Randomized Model for Communicating Embedded Systems
"... Nowadays, there is an intense research activity in designing systems that operate in real life, physical environments. This research is spanned by various areas in computer science and engineering: embedded systems, reactive systems, wireless communications, hybrid systems, stochastic processes, etc ..."
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Nowadays, there is an intense research activity in designing systems that operate in real life, physical environments. This research is spanned by various areas in computer science and engineering: embedded systems, reactive systems, wireless communications, hybrid systems, stochastic processes, etc. A severe limitation in the development of these systems is due to the mathematical foundation and complexity of the physical environment. Often, the physical environment is continuous and uncertain, and modelled in terms of continuous stochastic processes. These mathematics are quite different from the underlying mathematics of discrete controllers based on logic and algebra. In this paper, we propose a specification formalism called stochastic functional logic based on algebraic framework. This axiomatises and abstracts away advanced structures from functional and stochastic analysis. The definition of the logic mimics the practice in applied mathematics. This logic is integrated with a probabilistic process algebra to provide a specification framework for embedded systems. The integration mechanism is based on partial ordered sets. Moreover, we construct an energy integral to every stochastic functional logic specification. In this way, we combine the power of formal specification and stochastic analysis for the software development of embedded systems.
Extending Hybrid CSP with Probability and
"... Abstract. Probabilistic and stochastic behavior are omnipresent in computer controlled systems, in particular, so-called safety-critical hybrid systems, because of fundamental properties of nature, uncertain environments, or simplifications to overcome complexity. Tightly inter-twining discrete, con ..."
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Abstract. Probabilistic and stochastic behavior are omnipresent in computer controlled systems, in particular, so-called safety-critical hybrid systems, because of fundamental properties of nature, uncertain environments, or simplifications to overcome complexity. Tightly inter-twining discrete, continuous and stochastic dynamics complicates mod-elling, analysis and verification of stochastic hybrid systems (SHSs). In the literature, this issue has been extensively investigated, but unfortu-nately it still remains challenging as no promising general solutions are available yet. In this paper, we give our effort by proposing a general compositional approach for modelling and verification of SHSs. First, we extend Hybrid CSP (HCSP), a very expressive and process algebra-like formal modeling language for hybrid systems, by introducing probabil-ity and stochasticity to model SHSs, which is called stochastic HCSP (SHCSP). To this end, ordinary differential equations (ODEs) are gener-alized by stochastic differential equations (SDEs) and non-deterministic choice is replaced by probabilistic choice. Then, we extend Hybrid Hoare Logic (HHL) to specify and reason about SHCSP processes. We demon-strate our approach by an example from real-world. 1
