The monotone circuit complexity of boolean functions
نویسندگان
چکیده
منابع مشابه
The monotone circuit complexity of Boolean functions
Recently, Razborov obtained superpolynomial lower bounds for monotone circuits that lect cliques in graphs. In particular, Razborov showed that detecting cliques of size s in a graph dh m vertices requires monotone circuits of size .Q(m-'/(log m) ~') for fixed s, and size rn ao°~') for ,. :[log ml4J. In this paper we modify the arguments of Razborov to obtain exponential lower bounds for ,moton...
متن کاملMinimizing the Average Query Complexity of Learning Monotone Boolean Functions
This paper addresses the problem of completely reconstructing deterministic monotone Boolean functions via membership queries. The minimum average query complexity is guaranteed via recursion, where partially ordered sets (posets) make up the overlapping subproblems. For problems with up to 4 variables, the posets’ optimality conditions are summarized in the form of an evaluative criterion. The...
متن کاملCircuit Complexity and Multiplicative Complexity of Boolean Functions
In this note, we use lower bounds on Boolean multiplicative complexity to prove lower bounds on Boolean circuit complexity. We give a very simple proof of a 7n/3− c lower bound on the circuit complexity of a large class of functions representable by high degree polynomials over GF(2). The key idea of the proof is a circuit complexity measure assigning different weights to XOR and AND gates.
متن کاملInfluences of monotone Boolean functions
Recently, Keller and Pilpel conjectured that the influence of a monotone Boolean function does not decrease if we apply to it an invertible linear transformation. Our aim in this short note is to prove this conjecture.
متن کاملCeilings of Monotone Boolean Functions
This paper considers a particular relationship defined over pairs of n-argument monotone Boolean functions. The relationship is of interest since we can show that if ( g, h ) satisfy it then for any n-argument monotone Boolean function f there is a close relationship between the combinational and monotone network complexities of the function (f /\ g) \/ h. We characterise the class of pairs of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Combinatorica
سال: 1987
ISSN: 0209-9683,1439-6912
DOI: 10.1007/bf02579196