Robust Satisfiability of Systems of Equations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F15%3A00448097" target="_blank" >RIV/67985807:_____/15:00448097 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1145/2751524" target="_blank" >http://dx.doi.org/10.1145/2751524</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1145/2751524" target="_blank" >10.1145/2751524</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Robust Satisfiability of Systems of Equations

Popis výsledku v původním jazyce

We study the problem of robust satisfiability of systems of nonlinear equations, namely, whether for a given continuous function f:K --> R^n on a finite simplicial complex K and alpha > 0, it holds that each function g:K --> R^n such that ||g-f|| <= alpha, has a root in K. Via a reduction to the extension problem of maps into a sphere, we particularly show that this problem is decidable in polynomial time for every fixed n, assuming dim K <= 2n-3. This is a substantial extension of previous computational applications of topological degree and related concepts in numerical and interval analysis. Via a reverse reduction, we prove that the problem is undecidable when dim K >= 2n-2, where the threshold comes from the stable range in homotopy theory. For the lucidity of our exposition, we focus on the setting when f is simplexwise linear. Such functions can approximate general continuous functions, and thus we get approximation schemes and undecidability of the robust satisfiability in othe

Název v anglickém jazyce

Robust Satisfiability of Systems of Equations

Popis výsledku anglicky

We study the problem of robust satisfiability of systems of nonlinear equations, namely, whether for a given continuous function f:K --> R^n on a finite simplicial complex K and alpha > 0, it holds that each function g:K --> R^n such that ||g-f|| <= alpha, has a root in K. Via a reduction to the extension problem of maps into a sphere, we particularly show that this problem is decidable in polynomial time for every fixed n, assuming dim K <= 2n-3. This is a substantial extension of previous computational applications of topological degree and related concepts in numerical and interval analysis. Via a reverse reduction, we prove that the problem is undecidable when dim K >= 2n-2, where the threshold comes from the stable range in homotopy theory. For the lucidity of our exposition, we focus on the setting when f is simplexwise linear. Such functions can approximate general continuous functions, and thus we get approximation schemes and undecidability of the robust satisfiability in othe

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

IN - Informatika

OECD FORD obor

—

Projekt

<a href="/cs/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Centrum excelence - Institut teoretické informatiky (CE-ITI)</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of the ACM

ISSN

0004-5411

e-ISSN

—

Svazek periodika

62

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

19

Strana od-do

"Article 26"

Kód UT WoS článku

000361200500001

EID výsledku v databázi Scopus

2-s2.0-84942061019