234 research outputs found
On the complexity of bounded time and precision reachability for piecewise affine systems
Reachability for piecewise affine systems is known to be undecidable,
starting from dimension . In this paper we investigate the exact complexity
of several decidable variants of reachability and control questions for
piecewise affine systems. We show in particular that the region to region
bounded time versions leads to -complete or co--complete problems,
starting from dimension . We also prove that a bounded precision version
leads to -complete problems
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
Complexity of stability and controllability of elementary hybrid systems
Caption title.Includes bibliographical references (p. 16-18).Supported by ARO. DAAL-03-92-G-0115 Supported by NATO. CRG-961115Vincent D. Blondel, John N. Tsitsiklis
Reachability problems for PAMs
Piecewise affine maps (PAMs) are frequently used as a reference model to show
the openness of the reachability questions in other systems. The reachability
problem for one-dimentional PAM is still open even if we define it with only
two intervals. As the main contribution of this paper we introduce new
techniques for solving reachability problems based on p-adic norms and weights
as well as showing decidability for two classes of maps. Then we show the
connections between topological properties for PAM's orbits, reachability
problems and representation of numbers in a rational base system. Finally we
show a particular instance where the uniform distribution of the original orbit
may not remain uniform or even dense after making regular shifts and taking a
fractional part in that sequence.Comment: 16 page
The prospects for mathematical logic in the twenty-first century
The four authors present their speculations about the future developments of
mathematical logic in the twenty-first century. The areas of recursion theory,
proof theory and logic for computer science, model theory, and set theory are
discussed independently.Comment: Association for Symbolic Logi
Computability in planar dynamical systems
In this paper we explore the problem of computing attractors and
their respective basins of attraction for continuous-time planar dynamical
systems. We consider C1 systems and show that stability is in general
necessary (but may not be sufficient) to attain computability. In particular,
we show that (a) the problem of determining the number of attractors
in a given compact set is in general undecidable, even for analytic systems
and (b) the attractors are semi-computable for stable systems.
We also show that the basins of attraction are semi-computable if and
only if the system is stable
- …