On the negation-limited circuit complexity of merging Original Research Article

A negation-limited circuit is a combinational circuit that consists of AND, OR gates and a limited number of NOT gates. In this paper, we investigate the complexity of negation-limited circuits. The (n,n) merging function is a function that merges two presorted binary sequences x1⩽⋯⩽xn and y1⩽⋯⩽yn into a sequence z1⩽⋯⩽z2n. We prove that the size complexity of the (n,n) merging function with t=(log2 log2 n−a) NOT gates is Θ(2an).