ECCC-Report TR14-163https://eccc.weizmann.ac.il/report/2014/163Comments and Revisions published for TR14-163en-usSat, 29 Nov 2014 10:13:02 +0200
Paper TR14-163
| Homomorphism polynomials complete for VP |
Arnaud Durand,
Meena Mahajan,
Guillaume Malod,
Nicolas de Rugy-Altherre,
Nitin Saurabh
https://eccc.weizmann.ac.il/report/2014/163The VP versus VNP question, introduced by Valiant, is probably the most important open question in algebraic complexity theory. Thanks to completeness results, a variant of this question, VBP versus VNP, can be succinctly restated as asking whether the permanent of a generic matrix can be written as a determinant of a matrix of polynomially bounded size. Strikingly, this restatement does not mention any notion of computational model. To get a similar restatement for the original and more fundamental question, and also to better understand the class itself, we need a complete polynomial for VP. Ad hoc constructions yielding complete polynomials were known, but not natural examples in the vein of the determinant. We give here several variants of natural complete polynomials for VP, based on the notion of graph homomorphism polynomials.Sat, 29 Nov 2014 10:13:02 +0200https://eccc.weizmann.ac.il/report/2014/163