As a further step towards proving exponential lower bounds for general non-commutative circuits, we also extend our techniques to prove an exponential lower bound for a class of circuits which is a restriction of general non-commutative circuits and a generalization of non-commutative skew circuits. As far as we know, this is the strongest model of non-commutative computation for which we have superpolynomial lower bounds.
Joint work with Nutan Limaye and Srikanth Srinivasan.