6 research outputs found
Abstraction of Elementary Hybrid Systems by Variable Transformation
Elementary hybrid systems (EHSs) are those hybrid systems (HSs) containing
elementary functions such as exp, ln, sin, cos, etc. EHSs are very common in
practice, especially in safety-critical domains. Due to the non-polynomial
expressions which lead to undecidable arithmetic, verification of EHSs is very
hard. Existing approaches based on partition of state space or
over-approximation of reachable sets suffer from state explosion or inflation
of numerical errors. In this paper, we propose a symbolic abstraction approach
that reduces EHSs to polynomial hybrid systems (PHSs), by replacing all
non-polynomial terms with newly introduced variables. Thus the verification of
EHSs is reduced to the one of PHSs, enabling us to apply all the
well-established verification techniques and tools for PHSs to EHSs. In this
way, it is possible to avoid the limitations of many existing methods. We
illustrate the abstraction approach and its application in safety verification
of EHSs by several real world examples
From Electric Circuits to Chemical Networks
Electric circuits manipulate electric charge and magnetic flux via a small
set of discrete components to implement useful functionality over continuous
time-varying signals represented by currents and voltages. Much of the same
functionality is useful to biological organisms, where it is implemented by a
completely different set of discrete components (typically proteins) and signal
representations (typically via concentrations). We describe how to take a
linear electric circuit and systematically convert it to a chemical reaction
network of the same functionality, as a dynamical system. Both the structure
and the components of the electric circuit are dissolved in the process, but
the resulting chemical network is intelligible. This approach provides access
to a large library of well-studied devices, from analog electronics, whose
chemical network realization can be compared to natural biochemical networks,
or used to engineer synthetic biochemical networks