Monotone depth lower bound for st connectivity
نویسندگان
چکیده
In Lecture 2, we saw how communication complexity lower bounds yield lower bounds for circuit depth. In particular, we showed that for any function f , D(KWf ) = depth(f) and D(KW f ) = depth (f), where KWf denotes the Karchmer-Wigderson game on f . Using this, we showed that monotone circuits for matching require Ω(n) depth. In this lecture we will show that circuits solving directed s-t connectivity require Ω(log n) depth. The directed s-t connectivity function DSTCONn is defined as follows: Given a directed graph G on n nodes, a source vertex s and a target vertex t,
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تاریخ انتشار 2012