## Circuit Minimization Problem (1999)

Venue: | In ACM Symposium on Theory of Computing (STOC |

Citations: | 26 - 1 self |

### BibTeX

@INPROCEEDINGS{Kabanets99circuitminimization,

author = {Valentine Kabanets and Jin-yi Cai},

title = {Circuit Minimization Problem},

booktitle = {In ACM Symposium on Theory of Computing (STOC},

year = {1999},

pages = {73--79},

publisher = {ACM Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

We study the complexity of the circuit minimization problem: given the truth table of a Boolean function f and a parameter s, decide whether f can be realized by a Boolean circuit of size at most s. We argue why this problem is unlikely to be in P (or even in P=poly) by giving a number of surprising consequences of such an assumption. We also argue that proving this problem to be NP-complete (if it is indeed true) would imply proving strong circuit lower bounds for the class E, which appears beyond the currently known techniques. Keywords: hard Boolean functions, derandomization, natural properties, NP-completeness. 1 Introduction An n-variable Boolean function f n : f0; 1g n ! f0; 1g can be given by either its truth table of size 2 n , or a Boolean circuit whose size may be significantly smaller than 2 n . It is well known that most Boolean functions on n variables have circuit complexity at least 2 n =n [Sha49], but so far no family of sufficiently hard functions has ...