Anwar Adkhamovich Irmatov

On the number of threshold functions

Abstract A Boolean function is called a threshold function if its truth domain is a part of the n-cube cut off by some hyperplane. The number of threshold functions of n variables P(2, n) was estimated in [1, 2, 3]. Obtaining the lower bounds is a problem of special difficulty. Using a result of the paper [4], Zuev in [3] showed that for sufficiently large n P(2, n) > 2n²(1-10/ln n). In the present paper a new proof which gives a more precise lower bound of P(2, n) is proposed, namely, it is proved that for sufficiently large n P(2, n) > 2n²(1-7/ln n)P(2, [(7(n-1)ln2)/ln(n- 1)]).

Arrangements of Hyperplanes and the Number of Threshold Functions

AbstractTwo approaches on estimating the number of threshold functions which were recently developed by the author are discussed. Let P(K,n) denote the number of threshold functions in K-valued logic. The first approach establishes that

Method and mechanism for extraction and recognition of polygons in an ic design

P(K,n + 1) \geqslant \frac{1}{2}\left( {\mathop {K^{n - 1} }\limits_{\left\lfloor {n - 4 - 2\frac{n}{{\log _K n}}} \right\rfloor } } \right)P\left( {K,\left\lfloor {{\text{2}}\frac{n}{{\log _K n}} + 3} \right\rfloor } \right).

METHOD AND SYSTEM FOR AUTOMATED FACE DETECTION AND RECOGNITION

The key argument of investigation is the generalization of the result of Odlyzko on subspaces spanned by random selections of ±1-vectors. Let

Method and apparatus for prominent facial features recognition

E_K = \{ 0,1 \ldots ,K - 1\}

Face identification method and device thereof

and let E denote the set of all vectors