Non-commutative arithmetic circuits with division

  title={Non-commutative arithmetic circuits with division},
  author={Pavel Hrubes and Avi Wigderson},
We initiate the study of the complexity of arithmetic circuits with division gates over non-commuting variables. Such circuits and formulas compute <i>non-commutative</i> rational functions, which, despite their name, can no longer be expressed as ratios of polynomials. We prove some lower and upper bounds, completeness and simulation results, as follows. If <i>X</i> is <i>n</i> x <i>n</i> matrix consisting of <i>n</i><sup>2</sup> distinct mutually non-commuting variables, we show that: (<i>i… CONTINUE READING

From This Paper

Figures, tables, results, connections, and topics extracted from this paper.
0 Extracted Citations
4 Extracted References
Similar Papers

Referenced Papers

Publications referenced by this paper.
Showing 1-4 of 4 references

Free rings and their relations

  • P. M. Cohn
  • Academic Press
  • 1985
Highly Influential
8 Excerpts

Vermeidung von divisionen

  • V. Strassen
  • J. of Reine Angew. Math., 264:182–202
  • 1973
Highly Influential
10 Excerpts

Theory of noncommutative determinants

  • I. Gelfand, V. Retakh
  • and characteristic functions of graphs. Funct…
  • 1992
Highly Influential
6 Excerpts

Similar Papers

Loading similar papers…