Candidate Boolean Functions towards Super-Quadratic Formula Size

Kenya UENO
2015 IEICE transactions on information and systems  
In this paper, we explore possibilities and difficulties to prove super-quadratic formula size lower bounds from the following aspects. First, we consider recursive Boolean functions and prove their general formula size upper bounds. We also discuss recursive Boolean functions based on exact 2-bit functions. We show that their formula complexity are at least Ω(n 2 ). Hence they can be candidate Boolean functions to prove super-quadratic formula size lower bounds. Next, we consider the reason of
more » ... the difficulty of resolving the formula complexity of the majority function in contrast with the parity function. In particular, we discuss the structure of an optimal protocol partition for the Karchmer-Wigderson communication game. key words: Boolean function, computational complexity, formula complexity
doi:10.1587/transinf.2014fcp0011 fatcat:vdirtm3jkrhonofaoohtcvnho4