On the complexity of bounded time and precision reachability for piecewise affine systems

@article{Bazille2018OnTC,
  title={On the complexity of bounded time and precision reachability for piecewise affine systems},
  author={Hugo Bazille and Olivier Bournez and Walid E. Gomaa and Amaury Pouly},
  journal={Theor. Comput. Sci.},
  year={2018},
  volume={735},
  pages={132-146}
}
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Reachability problems in low-dimensional nondeterministic polynomial maps over integers

References

SHOWING 1-10 OF 14 REFERENCES
On The Complexity of Bounded Time Reachability for Piecewise Affine Systems
TLDR
It is shown that the region to region bounded time versions leads to NP-complete or co-NP-complete problems, starting from dimension 2.
Reachability Problems for Hierarchical Piecewise Constant Derivative Systems
TLDR
This paper shows a restriction of HPCDs (called RHPCDs) which leads to the reachability problem becoming decidable, and shows NP-hardness of reachability for nondeterministic RHPCD.
Reachability Analysis of Dynamical Systems Having Piecewise-Constant Derivatives
Widening the Boundary between Decidable and Undecidable Hybrid Systems
TLDR
It is shown that the reachable question for some two dimensional hybrid systems are undecidable and that for other 2-dim systems this question remains unanswered, showing that it is as hard as the reachability problem for Piecewise Affine Maps, that is a well known open problem.
On the Decidability of the Reachability Problem for Planar Differential Inclusions
TLDR
An algorithm for solving the reachability problem of two-dimensional piece-wise rectangular differential inclusions is developed based on the computation of the limit of individual trajectories and it is proved that there are only finitely many "qualitative types" of those trajectories.
What's decidable about hybrid automata?
TLDR
It is proved that the reachability problem is undecidable for timed automata augmented with a single stopwatch, and an (optimal) PSPACE reachability algorithm is given for the case of initialized rectangular automata.
Mortality of iterated piecewise affine functions over the integers: Decidability and complexity
TLDR
This paper establishes (un)decidability results for the integer setting, and shows that also over integers, undecidability (moreover, 0 completeness) begins at two dimensions.
Computability with Low-Dimensional Dynamical Systems
Computing over the Reals with Addition and Order
  • P. Koiran
  • Computer Science, Mathematics
    Theor. Comput. Sci.
  • 1994
Reducibility Among Combinatorial Problems
  • R. Karp
  • Computer Science
    50 Years of Integer Programming
  • 1972
TLDR
Throughout the 1960s I worked on combinatorial optimization problems including logic circuit design with Paul Roth and assembly line balancing and the traveling salesman problem with Mike Held, which made me aware of the importance of distinction between polynomial-time and superpolynomial-time solvability.
...
...