期刊名称:Electronic Colloquium on Computational Complexity
印刷版ISSN:1433-8092
出版年度:2020
卷号:2020
页码:1-26
出版社:Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要:The determinant is a canonical VBP-complete polynomial in the algebraic complexity setting. In this work, we introduce two variants of the determinant polynomial which we call StackDetnpXq and CountDetnpXq and show that they are VP and VNP complete respectively under p-projections. The definitions of the polynomials are inspired by a combinatorial characterisation of the determinant developed by Mahajan and Vinay (SODA 1997). We extend the combinatorial object in their work, namely clow sequences, by introducing additional edge labels on the edges of the underlying graph. The idea of using edge labels is inspired by the work of Mengel (MFCS 2013).