TU Berlin

Fachgebiet Algorithmische AlgebraProf. Dr. Peter Bürgisser

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Prof. Dr. Peter Bürgisser

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Technische Universität Berlin
Institut für Mathematik
Sekretariat MA 3-2
Straße des 17. Juni 136
10623 Berlin

Büro
Raum MA 317 (3. OG)
Institut für Mathematik

Kontakt

Sekretariat
Beate Nießen
Raum MA 318
Tel.: +49 (0)30 314 - 25771

eMail
peter.buergisser@offmath.tu-berlin.de

Telefon
+49 (0)30 314 - 75902
Faxgerät
+49 (0)30 314 - 25839

Sprechstunde
Während der Vorlesungszeit: Do, 15-16 Uhr.
Während der vorlesungsfreien Zeit: nach Vereinbarung.

Publikationen

Cook's versus Valiant's Hypothesis
Zitatschlüssel B-Cooks-Versus-Valiants-Hypothesis
Autor Peter Bürgisser
Seiten 71-88
Jahr 2000
Journal Theor. Comp. Sci.
Jahrgang 235
Zusammenfassung In 1979 Valiant developed a nonuniform algebraic analogue of the theory of NP-completeness for computations with polynomials over a field. This theory centers around his hypothesis VP <> VNP, the analogue of Cook's hypothesis P <> NP. We identify the Boolean parts of Valiant's algebraic complexity classes VP and VNP as familiar nonuniform complexity classes. As a consequence, we obtain rather strong evidence for Valiant's hypothesis: if it were wrong, then the nonuniform versions of NC and PH would be equal. In particular, the polynomial hierarchy would collapse to the second level. We show this for fields of characteristic zero and finite fields; in the first case we assume a generalized Riemann hypothesis. The crucial step in our proof is the elimination of constants in the field, which relies on a recent method developed by Koiran (1996).
Link zur Publikation Download Bibtex Eintrag

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