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.
Elsevier Science Publishers B. V., Netherlands
oai:noad.sci.am:136088
Institute for Informatics and Automation Problems
Apr 9, 2021
Apr 9, 2021
36
https://noad.sci.am/publication/149570
Edition name | Date |
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Levon Aslanyan, The splitting technique in monotone recognition | Apr 9, 2021 |
Aslanyan Levon Topchyan Vardan Danoyan Haykaz
Aslanyan Levon Topchyan Vardan
Aslanyan Levon Gronau Hans-Dietrich SahakyanHasmik Wagner Peter
Aslanyan Levon Sahakyan Hasmik Romanov Vladimir Da Costa Georges Kacimi Rahim