Parallel Identity Testing for Skew Circuits with Big Powers and Applications

  • Daniel KönigEmail author
  • Markus Lohrey
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9235)


Powerful skew arithmetic circuits are introduced. These are skew arithmetic circuits with variables, where input gates can be labelled with powers \(x^n\) for binary encoded numbers n. It is shown that polynomial identity testing for powerful 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 belongs to \(\mathsf {coRNC}^2\). Full proofs can be found in the long version [13].


Word Problem Polynomial Ring Wreath Product Edge Label Multiplication Gate 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Universität SiegenSiegenGermany

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