Deutsch
 
Hilfe Datenschutzhinweis Impressum
  DetailsucheBrowse

Datensatz

 
 
DownloadE-Mail
  On the Decidability of Termination for Polynomial Loops

Frohn, F., Hark, M., & Giesl, J. (2019). On the Decidability of Termination for Polynomial Loops. Retrieved from https://arxiv.org/abs/1910.11588.

Item is

Basisdaten

einblenden: ausblenden:
Genre: Forschungspapier

Dateien

einblenden: Dateien
ausblenden: Dateien
:
arXiv:1910.11588.pdf (Preprint), 455KB
Name:
arXiv:1910.11588.pdf
Beschreibung:
File downloaded from arXiv at 2021-01-22 09:49
OA-Status:
Sichtbarkeit:
Öffentlich
MIME-Typ / Prüfsumme:
application/pdf / [MD5]
Technische Metadaten:
Copyright Datum:
-
Copyright Info:
-

Externe Referenzen

einblenden:

Urheber

einblenden:
ausblenden:
 Urheber:
Frohn, Florian1, Autor           
Hark, Marcel2, Autor
Giesl, Jürgen2, Autor
Affiliations:
1Automation of Logic, MPI for Informatics, Max Planck Society, ou_1116545              
2External Organizations, ou_persistent22              

Inhalt

einblenden:
ausblenden:
Schlagwörter: Computer Science, Logic in Computer Science, cs.LO
 Zusammenfassung: We consider the termination problem for triangular weakly non-linear loops
(twn-loops) over some ring $\mathcal{S}$ like $\mathbb{Z}$, $\mathbb{Q}$, or
$\mathbb{R}$. Essentially, the guard of such a loop is an arbitrary Boolean
formula over (possibly non-linear) polynomial inequations, and the body is a
single assignment $(x_1, \ldots, x_d) \longleftarrow (c_1 \cdot x_1 + p_1,
\ldots, c_d \cdot x_d + p_d)$ where each $x_i$ is a variable, $c_i \in
\mathcal{S}$, and each $p_i$ is a (possibly non-linear) polynomial over
$\mathcal{S}$ and the variables $x_{i+1},\ldots,x_{d}$. We present a reduction
from the question of termination to the existential fragment of the first-order
theory of $\mathcal{S}$ and $\mathbb{R}$. For loops over $\mathbb{R}$, our
reduction entails decidability of termination. For loops over $\mathbb{Z}$ and
$\mathbb{Q}$, it proves semi-decidability of non-termination.
Furthermore, we present a transformation to convert certain non-twn-loops
into twn-form. Then the original loop terminates iff the transformed loop
terminates over a specific subset of $\mathbb{R}$, which can also be checked
via our reduction. This transformation also allows us to prove tight complexity
bounds for the termination problem for two important classes of loops which can
always be transformed into twn-loops.

Details

einblenden:
ausblenden:
Sprache(n): eng - English
 Datum: 2019-10-252020-09-152019
 Publikationsstatus: Online veröffentlicht
 Seiten: 34 p.
 Ort, Verlag, Ausgabe: -
 Inhaltsverzeichnis: -
 Art der Begutachtung: -
 Identifikatoren: arXiv: 1910.11588
URI: https://arxiv.org/abs/1910.11588
BibTex Citekey: Frohn_arXiv1910.11588
 Art des Abschluß: -

Veranstaltung

einblenden:

Entscheidung

einblenden:

Projektinformation

einblenden:

Quelle

einblenden: