Emptiness Problems for Integer Circuits

Barth, Dominik; Beck, Moritz; Dose, Titus; Glaßer, Christian; Michler, Larissa; Technau, Marc

Emptiness Problems for Integer Circuits

Dateien

Zu diesem Dokument gibt es keine Dateien.

Datum

2017

Autor:innen

Barth, Dominik

Beck, Moritz

Dose, Titus

Glaßer, Christian

Michler, Larissa

Technau, Marc

Sammlungen

Informatik und Informationswissenschaft

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

Electronic Colloquium on Computational Complexity. 2017(12), TR17-012. ISSN 1433-8092

Zusammenfassung

We study the computational complexity of emptiness problems for circuits over sets of natural numbers with the operations union, intersection, complement, addition, and multiplication. For most settings of allowed operations we precisely characterize the complexity in terms of completeness for classes like NL, NP, and PSPACE. The case where intersection, addition, and multiplication is allowed turns out to be equivalent to the complement of polynomial identity testing (PIT). Our results imply the following improvements and insights on problems studied in earlier papers. We improve the bounds for the membership problem MC(∪;∩;‾;+;x) studied by McKenzie and Wagner 2007 and for the equivalence problem EQ(∪;∩;‾;+;x) studied by Gla_er et al. 2010. Moreover, it turns out that the following problems are equivalent to PIT, which shows that the challenge to improve their bounds is just a reformulation of a well-studied, major open problem in algebraic computing complexity:
- membership problem MC(∩;+;x) studied by McKenzie and Wagner 2007
- integer membership problems MC_ℤ (+;x), MC_ℤ (∩;+;x) studied by Travers 2006
- equivalence problem EQ(+;x) studied by Glaßer et al. 2010

Fachgebiet (DDC)

004 Informatik

Schlagwörter

computational complexity, integer circuits, Integer expressions, polynomial identity testing

Zitieren

ISO 690

BARTH, Dominik, Moritz BECK, Titus DOSE, Christian GLASSER, Larissa MICHLER, Marc TECHNAU, 2017. Emptiness Problems for Integer Circuits. In: Electronic Colloquium on Computational Complexity. 2017(12), TR17-012. ISSN 1433-8092

BibTex

@article{Barth2017Empti-44630,
  year={2017},
  title={Emptiness Problems for Integer Circuits},
  url={https://eccc.weizmann.ac.il/report/2017/012/},
  number={12},
  issn={1433-8092},
  journal={Electronic Colloquium on Computational Complexity},
  author={Barth, Dominik and Beck, Moritz and Dose, Titus and Glaßer, Christian and Michler, Larissa and Technau, Marc},
  note={Article Number: TR17-012}
}

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URL der Originalveröffentl.

https://eccc.weizmann.ac.il/report/2017/012/

Prüfdatum der URL

2019-01-11

Universitätsbibliographie

Nein