1,310 research outputs found
A Survey on Continuous Time Computations
We provide an overview of theories of continuous time computation. These
theories allow us to understand both the hardness of questions related to
continuous time dynamical systems and the computational power of continuous
time analog models. We survey the existing models, summarizing results, and
point to relevant references in the literature
Completeness of Lyapunov Abstraction
In this work, we continue our study on discrete abstractions of dynamical
systems. To this end, we use a family of partitioning functions to generate an
abstraction. The intersection of sub-level sets of the partitioning functions
defines cells, which are regarded as discrete objects. The union of cells makes
up the state space of the dynamical systems. Our construction gives rise to a
combinatorial object - a timed automaton. We examine sound and complete
abstractions. An abstraction is said to be sound when the flow of the time
automata covers the flow lines of the dynamical systems. If the dynamics of the
dynamical system and the time automaton are equivalent, the abstraction is
complete.
The commonly accepted paradigm for partitioning functions is that they ought
to be transversal to the studied vector field. We show that there is no
complete partitioning with transversal functions, even for particular dynamical
systems whose critical sets are isolated critical points. Therefore, we allow
the directional derivative along the vector field to be non-positive in this
work. This considerably complicates the abstraction technique. For
understanding dynamical systems, it is vital to study stable and unstable
manifolds and their intersections. These objects appear naturally in this work.
Indeed, we show that for an abstraction to be complete, the set of critical
points of an abstraction function shall contain either the stable or unstable
manifold of the dynamical system.Comment: In Proceedings HAS 2013, arXiv:1308.490
O-Minimal Hybrid Reachability Games
In this paper, we consider reachability games over general hybrid systems,
and distinguish between two possible observation frameworks for those games:
either the precise dynamics of the system is seen by the players (this is the
perfect observation framework), or only the starting point and the delays are
known by the players (this is the partial observation framework). In the first
more classical framework, we show that time-abstract bisimulation is not
adequate for solving this problem, although it is sufficient in the case of
timed automata . That is why we consider an other equivalence, namely the
suffix equivalence based on the encoding of trajectories through words. We show
that this suffix equivalence is in general a correct abstraction for games. We
apply this result to o-minimal hybrid systems, and get decidability and
computability results in this framework. For the second framework which assumes
a partial observation of the dynamics of the system, we propose another
abstraction, called the superword encoding, which is suitable to solve the
games under that assumption. In that framework, we also provide decidability
and computability results
Algorithmic Verification of Continuous and Hybrid Systems
We provide a tutorial introduction to reachability computation, a class of
computational techniques that exports verification technology toward continuous
and hybrid systems. For open under-determined systems, this technique can
sometimes replace an infinite number of simulations.Comment: In Proceedings INFINITY 2013, arXiv:1402.661
Re-verification of a Lip Synchronization Protocol using Robust Reachability
The timed automata formalism is an important model for specifying and
analysing real-time systems. Robustness is the correctness of the model in the
presence of small drifts on clocks or imprecision in testing guards. A symbolic
algorithm for the analysis of the robustness of timed automata has been
implemented. In this paper, we re-analyse an industrial case lip
synchronization protocol using the new robust reachability algorithm. This lip
synchronization protocol is an interesting case because timing aspects are
crucial for the correctness of the protocol. Several versions of the model are
considered: with an ideal video stream, with anchored jitter, and with
non-anchored jitter
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