Quasi-Decidability of a Fragment of the First-Order Theory of Real Numbers

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F16%3A00449388" target="_blank" >RIV/67985807:_____/16:00449388 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s10817-015-9351-3" target="_blank" >http://dx.doi.org/10.1007/s10817-015-9351-3</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10817-015-9351-3" target="_blank" >10.1007/s10817-015-9351-3</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Quasi-Decidability of a Fragment of the First-Order Theory of Real Numbers

Popis výsledku v původním jazyce

In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of n equations in n variables, and for which all functions are computable in the sense that it is possible to compute arbitrarily close interval approximations. Even though this fragment is undecidable, we prove that - under the additional assumption of bounded domains-there is a (possibly non-terminating) algorithm for checking satisfiability such that (1) whenever it terminates, it computes a correct answer, and (2) it always terminates when the input is robust. A formula is robust, if its satisfiability does not change under small continuous perturbations. We also prove that it is not possible to generalize this result to the full first-order language - removing the restriction on the number of equations versus number of variables. As a basic tool for our algorithm we use the notion of degree from the field of topology.

Název v anglickém jazyce

Quasi-Decidability of a Fragment of the First-Order Theory of Real Numbers

Popis výsledku anglicky

In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of n equations in n variables, and for which all functions are computable in the sense that it is possible to compute arbitrarily close interval approximations. Even though this fragment is undecidable, we prove that - under the additional assumption of bounded domains-there is a (possibly non-terminating) algorithm for checking satisfiability such that (1) whenever it terminates, it computes a correct answer, and (2) it always terminates when the input is robust. A formula is robust, if its satisfiability does not change under small continuous perturbations. We also prove that it is not possible to generalize this result to the full first-order language - removing the restriction on the number of equations versus number of variables. As a basic tool for our algorithm we use the notion of degree from the field of topology.

Druh

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

CEP obor

IN - Informatika

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2016

Kód důvěrnosti údajů

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

Název periodika

Journal of Automated Reasoning

ISSN

0168-7433

e-ISSN

—

Svazek periodika

57

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

29

Strana od-do

157-185

Kód UT WoS článku

000379256400003

EID výsledku v databázi Scopus

2-s2.0-84944699064