2012 27th Annual IEEE Symposium on Logic in Computer Science 2012
DOI: 10.1109/lics.2012.13
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Logics of Dynamical Systems

Abstract: 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… Show more

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Cited by 88 publications
(122 citation statements)
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References 134 publications
(397 reference statements)
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“…Fundamentally, however, the study of the safety of hybrid systems can be shown to reduce constructively to the problem of generating invariants for their differential equations [18]. We focus on this core problem in this paper.…”
Section: Introductionmentioning
confidence: 99%
“…Fundamentally, however, the study of the safety of hybrid systems can be shown to reduce constructively to the problem of generating invariants for their differential equations [18]. We focus on this core problem in this paper.…”
Section: Introductionmentioning
confidence: 99%
“…We model our system using Differential Dynamic Logic dL [Pla08,Pla10,Pla12], a logic for reasoning about hybrid programs. dL allows discrete assignments, control structures, and execution of differential equations.…”
Section: Differential Dynamic Logic and Keymaeramentioning
confidence: 99%
“…Hybrid dynamical systems [2,12] are mathematical models for analyzing the interaction between discrete and continuous dynamics.…”
Section: Introductionmentioning
confidence: 99%
“…Hybrid automata are not conducive to compositional reasoning; to establish a property about a hybrid automaton, it does not suffice to establish that property about each component of a decomposed system. Hybrid programs [10,11,12], in contrast, are a compositional programming language model of hybrid dynamics. They extend regular programs with differential equations.…”
Section: Introductionmentioning
confidence: 99%
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