DROPS

Document

Complexity of Symbolic and Numerical Problems (Dagstuhl Seminar 15242)

Authors: Peter Bürgisser, Felipe Cucker, Marek Karpinski, and Nicolai Vorobjov

Published in: Dagstuhl Reports, Volume 5, Issue 6 (2016)

Abstract

This report documents the program and the outcomes of Dagstuhl Seminar 15242 "Complexity of Symbolic and Numerical Problems".

Cite as

Peter Bürgisser, Felipe Cucker, Marek Karpinski, and Nicolai Vorobjov. Complexity of Symbolic and Numerical Problems (Dagstuhl Seminar 15242). In Dagstuhl Reports, Volume 5, Issue 6, pp. 28-47, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

Copy BibTex To Clipboard

@Article{burgisser_et_al:DagRep.5.6.28,
  author =	{B\"{u}rgisser, Peter and Cucker, Felipe and Karpinski, Marek and Vorobjov, Nicolai},
  title =	{{Complexity of Symbolic and Numerical Problems (Dagstuhl Seminar 15242)}},
  pages =	{28--47},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2016},
  volume =	{5},
  number =	{6},
  editor =	{B\"{u}rgisser, Peter and Cucker, Felipe and Karpinski, Marek and Vorobjov, Nicolai},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.5.6.28},
  URN =		{urn:nbn:de:0030-drops-55066},
  doi =		{10.4230/DagRep.5.6.28},
  annote =	{Keywords: Symbolic computation, Algorithms in real algebraic geometry, Complexity lower bounds, Geometry of numerical algorithms}
}

Document

DOI: 10.4230/DagSemProc.06021.10

Upper and Lower Bounds on Sizes of Finite Bisimulations of Pfaffian Dynamical Systems

Authors: Margarita Korovina and Nicolai Vorobjov

Published in: Dagstuhl Seminar Proceedings, Volume 6021, Reliable Implementation of Real Number Algorithms: Theory and Practice (2006)

Abstract

In this paper we study a class of dynamical systems defined by Pfaffian maps. It is a sub-class of o-minimal dynamical systems which capture rich continuous dynamics and yet can be studied using finite bisimulations. The existence of finite bisimulations for o-minimal dynamical and hybrid systems has been shown by several authors; see e.g. Brihaye et al (2004), Davoren (1999), Lafferriere et al (2000). The next natural question to investigate is how the sizes of such bisimulations can be bounded. The first step in this direction was done by Korovina et al (2004) where a double exponential upper bound was shown for Pfaffian dynamical and hybrid systems. In the present paper we improve this bound to a single exponential upper bound. Moreover we show that this bound is tight in general, by exhibiting a parameterized class of systems on which the exponential bound is attained. The bounds provide a basis for designing efficient algorithms for computing bisimulations, solving reachability and motion planning problems.

Cite as

Margarita Korovina and Nicolai Vorobjov. Upper and Lower Bounds on Sizes of Finite Bisimulations of Pfaffian Dynamical Systems. In Reliable Implementation of Real Number Algorithms: Theory and Practice. Dagstuhl Seminar Proceedings, Volume 6021, pp. 1-18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

Copy BibTex To Clipboard

@InProceedings{korovina_et_al:DagSemProc.06021.10,
  author =	{Korovina, Margarita and Vorobjov, Nicolai},
  title =	{{Upper and Lower Bounds on Sizes of Finite Bisimulations of Pfaffian Dynamical Systems}},
  booktitle =	{Reliable Implementation of Real Number Algorithms: Theory and Practice},
  pages =	{1--18},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6021},
  editor =	{Peter Hertling and Christoph M. Hoffmann and Wolfram Luther and Nathalie Revol},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06021.10},
  URN =		{urn:nbn:de:0030-drops-7130},
  doi =		{10.4230/DagSemProc.06021.10},
  annote =	{Keywords: Hybrid systems, Pfaffian functions, bisimulation}
}

Search Results

Documents authored by Vorobjov, Nicolai

Complexity of Symbolic and Numerical Problems (Dagstuhl Seminar 15242)

Abstract

Cite as

Upper and Lower Bounds on Sizes of Finite Bisimulations of Pfaffian Dynamical Systems

Abstract

Cite as

Thanks for your feedback!

Could not send message