One of the major open problems in complexity theory is to demonstrate an explicit function which requires super logarithmic depth, to tackle this problem Karchmer, Raz and Wigderson proposed the KRW conjecture about composition of two functions. While this conjecture seems out of our current reach, some relaxed conjectures are ... more >>>

In this work, we study the natural monotone analogues of various equivalent definitions of VPSPACE: a well studied class (Poizat 2008, Koiran & Perifel 2009, Malod 2011, Mahajan & Rao 2013) that is believed to be larger than VNP. We observe that these monotone analogues are not equivalent unlike their ... more >>>

Guruswami and Smith (J. ACM 2016) considered codes for channels that are poly-size circuits which modify at most a $p$-fraction of the bits of the codeword. This class of channels is significantly stronger than Shannon's binary symmetric channel (BSC), but weaker than Hamming's channels which are computationally unbounded.

The goal ... more >>>