E.A. Okol'nishnikiva

Some operations over Boolean functions are considered. It is shown that

the operation of the geometrical projection and the operation of the

monotone extension can increase the complexity of Boolean functions for

formulas in each finite basis, for switching networks, for branching

programs, and read-$k$-times ...
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Dmytro Gavinsky, Or Meir, Omri Weinstein, Avi Wigderson

One of the major open problems in complexity theory is proving super-polynomial lower bounds for circuits with logarithmic depth (i.e., $\mathbf{P}\not\subseteq\mathbf{NC}_1~$). This problem is interesting for two reasons: first, it is tightly related to understanding the power of parallel computation and of small-space computation; second, it is one of the ... more >>>

Toniann Pitassi, Robert Robere

For a universal constant $\alpha > 0$, we prove size lower bounds of $2^{\alpha N}$ for computing an explicit monotone function in NP in the following models of computation: monotone formulas, monotone switching networks, monotone span programs, and monotone comparator circuits, where $N$ is the number of variables of the ... more >>>

Pranjal Dutta, Nitin Saxena, Amit Sinhababu

Newton iteration (NI) is an almost 350 years old recursive formula that approximates a simple root of a polynomial quite rapidly. We generalize it to a matrix recurrence (allRootsNI) that approximates all the roots simultaneously. In this form, the process yields a better circuit complexity in the case when the ... more >>>