Sunil K S, Balagopal Komarath, Jayalal Sarma

Comparator circuit model was originally introduced by Mayr and Subramanian (1992) to capture problems which are not known to be P-complete but still not known to admit efficient parallel algorithms. The class CC is the complexity class of problems many-one logspace reducible to the Comparator Circuit Value Problem We know ... more >>>

Stephen A. Cook, Toniann Pitassi, Robert Robere, Benjamin Rossman

Monotone span programs are a linear-algebraic model of computation which were introduced by Karchmer and Wigderson in 1993. They are known to be equivalent to linear secret sharing schemes, and have various applications in complexity theory and cryptography. Lower bounds for monotone span programs have been difficult to obtain because ... 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 >>>

Anna Gal, Robert Robere

Comparator circuits are a natural circuit model for studying the concept of bounded fan-out computations, which intuitively corresponds to whether or not a computational model can make "copies" of intermediate computational steps. Comparator circuits are believed to be weaker than general Boolean circuits, but they can simulate Branching Programs and ... more >>>