TY - GEN
A1 - Aslanyan Levon
A2 - Sahakyan Hasmik
PB - Elsevier
N2 - We consider the problem of query based algorithmic identification/recognition of monotone Boolean functions, as well as of binary functions defined on multi-valued discrete grids. Hansel's chain-split technique of n -cubes is a well known effective tool of monotone Boolean recognition. An extension by Alekseev is already applied to the grid case. The practical monotone recognition on n -cubes is provided by the so called chain-computation algorithms that is not extended to the case of multi-valued grids. We propose a novel split construction based on partitioning the grid into sub-grids and into discrete structures that are isomorphic to binary cubes. Monotonicity in a multi-valued grid implies monotonicity in all induced binary cubes and in multi-valued sub-grids. Applying Hansel's technique for identification of monotone Boolean functions on all appearing binary cubes, and Alekseev's algorithm on all sub-grids leads to different scenarios of reconstruction of monotone functions. On one hand such partitioning technique makes parallel recognition possible, on the other hand - the method can be used in practical identification algorithms due to simple structures and easily calculable quantities appearing after the partition to the n -cubes. Complexity issues of considered algorithms were also elaborated.
L1 - http://noad.sci.am/Content/136088/1-s2.0-S0166218X16301676-main.pdf
L2 - http://noad.sci.am/Content/136088
CY - Elsevier Science Publishers B. V., Netherlands
T1 - The splitting technique in monotone recognition
UR - http://noad.sci.am/dlibra/docmetadata?id=136088
ER -