Arithmetizing Classes Around NC1 and L

  • Nutan Limaye
  • Meena Mahajan
  • B. V. Raghavendra Rao
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4393)


The parallel complexity class NC1 has many equivalent models such as bounded width branching programs. Caussinus [10] considered arithmetizations of two of these classes, #NC1 and #BWBP. We further this study to include arithmetization of other classes. In particular, we show that counting paths in branching programs over visibly pushdown automata has the same power as #BWBP, while counting proof-trees in logarithmic width formulae has the same power as #NC1. We also consider polynomial-degree restrictions of \({\sf SC}^{i}\), denoted \({\sf sSC}^{i}\), and show that the Boolean class \({\sf sSC}{^1}\) lies between NC1 and L, whereas \({\sf sSC}^0\) equals \({\sf NC}^1\). On the other hand, \({\sf \#}{\sf sSC}^0\) contains #BWBP and is contained in FL, and #sSC1 contains #NC1 and is in \({\sf SC}^{2}\). We also investigate some closure properties of the newly defined arithmetic classes.


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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Nutan Limaye
    • 1
  • Meena Mahajan
    • 1
  • B. V. Raghavendra Rao
    • 1
  1. 1.The Institute of Mathematical Sciences, Chennai 600 113India

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