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In this paper we discuss the computational power of Lipschitz dynamical systems which are robust to in nitesimal perturbations. Whereas the study in [1] was done only for not-so-natural systems from a classical mathematical point of view (discontinuous di erential equation systems, discontinuous piecewise a ne 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 in nitesimal perturbations) is co-recursively enumerable for this kind of systems. Using this result we show that if robustness to in nitesimal perturbations is also required, the reachability problem becomes decidable. This result can be interpreted in the following manner: undecidability of veri cation doesn't hold for Lipschitz, computable and robust systems. We also show that the perturbed reachability problem is co-r.e. complete even for C1-systems.

Pertenece a

Sapientia Repositório Institucional Universidade do Algarve  


Bournez, Olivier -  Graça, Daniel -  Hainry, Emmanuel - 

Id.: 55204972

Idioma: eng  - 

Versión: 1.0

Estado: Final

Palabras claveVeri cation - 

Tipo de recurso: bookPart  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

Estructura: Atomic

Coste: no

Copyright: sí

: openAccess

Requerimientos técnicos:  Browser: Any - 

Relación: [References] Lecture Notes in Computer Science ARCoSS (Advanced Research in Computing and Software Science);6281
[References] http://www.springerlink.com/content/pux2120952u4207t/

Fecha de contribución: 05-dic-2013



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