1,907 research outputs found
Towards Physical Hybrid Systems
Some hybrid systems models are unsafe for mathematically correct but
physically unrealistic reasons. For example, mathematical models can classify a
system as being unsafe on a set that is too small to have physical importance.
In particular, differences in measure zero sets in models of cyber-physical
systems (CPS) have significant mathematical impact on the mathematical safety
of these models even though differences on measure zero sets have no tangible
physical effect in a real system. We develop the concept of "physical hybrid
systems" (PHS) to help reunite mathematical models with physical reality. We
modify a hybrid systems logic (differential temporal dynamic logic) by adding a
first-class operator to elide distinctions on measure zero sets of time within
CPS models. This approach facilitates modeling since it admits the verification
of a wider class of models, including some physically realistic models that
would otherwise be classified as mathematically unsafe. We also develop a proof
calculus to help with the verification of PHS.Comment: CADE 201
An Axiomatic Approach to Liveness for Differential Equations
This paper presents an approach for deductive liveness verification for
ordinary differential equations (ODEs) with differential dynamic logic.
Numerous subtleties complicate the generalization of well-known discrete
liveness verification techniques, such as loop variants, to the continuous
setting. For example, ODE solutions may blow up in finite time or their
progress towards the goal may converge to zero. Our approach handles these
subtleties by successively refining ODE liveness properties using ODE
invariance properties which have a well-understood deductive proof theory. This
approach is widely applicable: we survey several liveness arguments in the
literature and derive them all as special instances of our axiomatic refinement
approach. We also correct several soundness errors in the surveyed arguments,
which further highlights the subtlety of ODE liveness reasoning and the utility
of our deductive approach. The library of common refinement steps identified
through our approach enables both the sound development and justification of
new ODE liveness proof rules from our axioms.Comment: FM 2019: 23rd International Symposium on Formal Methods, Porto,
Portugal, October 9-11, 201
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