TY - GEN
T1 - Formulas are exponentially stronger than monotone circuits in non-commutative setting
AU - Hrube, Pavel
AU - Yehudayoff, Amir
PY - 2013
Y1 - 2013
N2 - We give an example of a non-commutative mono-tone polynomial f which can be computed by a polynomial-size non-commutative formula, but every monotone non-commutative circuit computing f must have an exponential size. In the non-commutative setting this gives, a fortiori, an exponential separation between monotone and general formulas, monotone and general branching programs, and monotone and general circuits. This answers some questions raised by Nisan.
AB - We give an example of a non-commutative mono-tone polynomial f which can be computed by a polynomial-size non-commutative formula, but every monotone non-commutative circuit computing f must have an exponential size. In the non-commutative setting this gives, a fortiori, an exponential separation between monotone and general formulas, monotone and general branching programs, and monotone and general circuits. This answers some questions raised by Nisan.
KW - algebraic complexity
KW - disjointness
KW - monotone computation
UR - https://www.scopus.com/pages/publications/84885670797
U2 - 10.1109/CCC.2013.11
DO - 10.1109/CCC.2013.11
M3 - Conference contribution
SN - 9780769549972
T3 - Proceedings of the Annual IEEE Conference on Computational Complexity
SP - 10
EP - 14
BT - Proceedings - 2013 IEEE Conference on Computational Complexity, CCC 2013
T2 - 2013 IEEE Conference on Computational Complexity, CCC 2013
Y2 - 5 June 2013 through 7 June 2013
ER -