Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Porful skew arithmetic circuits are introduced. These are skew arithmetic circuits with variables, where input gates can be labelled with pors $x^n$ for binary encoded numbers $n$. It is shown that polynomial identity testing for porful skew arithmetic circuits belongs to $\mathsf{coRNC}^2$, which generalizes a corresponding result for (standard) skew circuits. Two applications of this result are presented: (i) Equivalence of higher-dimensional straight-line programs can be tested in $\mathsf{coRNC}^2$; this result is even new in the one-dimensional case, where the straight-line programs produce strings. (ii) The compressed word problem (or circuit evaluation problem) for certain wreath products of finitely generated abelian groups belongs to $\mathsf{coRNC}^2$.
['Daniel König', 'Markus Lohrey']
I am writing a research paper on a idea Parallel Identity Testing for Skew Circuits with Big Powers and Applications
[{"from": "human", "value": "I am writing a research paper on a idea Parallel Identity Testing for Skew Circuits with Big Powers and Applications"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Porful skew arithmetic circuits are introduced. These are skew arithmetic circuits with variables, where input gates can be labelled with pors $x^n$ for binary encoded numbers $n$. It is shown that polynomial identity testing for porful skew arithmetic circuits belongs to $\\mathsf{coRNC}^2$, which generalizes a corresponding result for (standard) skew circuits. Two applications of this result are presented: (i) Equivalence of higher-dimensional straight-line programs can be tested in $\\mathsf{coRNC}^2$; this result is even new in the one-dimensional case, where the straight-line programs produce strings. (ii) The compressed word problem (or circuit evaluation problem) for certain wreath products of finitely generated abelian groups belongs to $\\mathsf{coRNC}^2$."}]