Complexity theory of real functions
Complexity theory of real functions
Reachability analysis of dynamical systems having piecewise-constant derivatives
Theoretical Computer Science - Special issue on hybrid systems
On the computational power of dynamical systems and hybrid systems
Theoretical Computer Science - Special issue on universal machines and computations
What's decidable about hybrid automata?
Journal of Computer and System Sciences
Computable analysis: an introduction
Computable analysis: an introduction
Automata For Modeling Real-Time Systems
ICALP '90 Proceedings of the 17th International Colloquium on Automata, Languages and Programming
Dynamical Properties of Timed Automata
FTRTFT '98 Proceedings of the 5th International Symposium on Formal Techniques in Real-Time and Fault-Tolerant Systems
Robust Undecidability of Timed and Hybrid Systems
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Analysis of Hybrid Systems: An Ounce of Realism Can Save an Infinity of States
CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
Perturbed Turing Machines and Hybrid Systems
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Continuity and computability of reachable sets
Theoretical Computer Science
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Robust simulations of turing machines with analytic maps and flows
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
Sensitivity analysis using type-based constraints
Proceedings of the 1st annual workshop on Functional programming concepts in domain-specific languages
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In this paper we discuss the computational power of Lipschitz dynamical systems which are robust to infinitesimal perturbations. Whereas the study in [1] was done only for not-so-natural systems from a classical mathematical point of view (discontinuous differential equation systems, discontinuous piecewise affine maps, or perturbed Turing machines), we prove that the results presented there can be generalized to Lipschitz and computable dynamical systems. In other words, we prove that the perturbed reachability problem (i.e. the reachability problem for systems which are subjected to infinitesimal perturbations) is co-recursively enumerable for this kind of systems. Using this result we show that if robustness to infinitesimal perturbations is also required, the reachability problem becomes decidable. This result can be interpreted in the following manner: undecidability of verification doesn't hold for Lipschitz, computable and robust systems. We also show that the perturbed reachability problem is co-r.e. complete even for C∞-systems.