A Lower Bound for the Monotone Depth of Connectivity
نویسنده
چکیده
plexity method is not well suited to resolving this question. On the other hand, Razborov's approximation method also does not seem suitable, since so far it has been applied mainly to prove superpolynomial bounds for monotone circuits, while U C O N N , can be computed by polynomial-size monotone circuits. We show that any monotone circuit for computing graph connectivity must have a depth greater than R ( ( l ~ g n ) ~ / ~ / loglogn). This proves that U C O N N , is not in monotone NC'. The proof technique, which is an adaptation of Razborov's approximation method, is also used to derive lower bounds for a general class of graph problems. In this paper, we prove lower bounds on the depth of monotone circuits for a In particular, we show that U C O N N , is not in monotone N C 1 . Surprisingly, this is done by an (nontrivial) of graph
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