Object recognition method based on logical correcting functions
Abstract
The article discusses the logical method of object recognition and the construction of corrective functions. To construct a logical method for classifying objects, the method for constructing the optimal continuation of logical correcting functions is used. An algorithm for the optimal continuation of logical correcting functions is constructed and an estimate of the complexity of the constructed algorithm is calculated. A theorem is proved that the search algorithm for the minimum upper zero of a Boolean monotone function μ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</sub> (y <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , y <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , ..., y <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> ) is in one-to-one correspondence with the problem of finding a minimal set of variables that is essential for a function F(x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , ..., x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> ) that is not defined everywhere.