Levon Aslanyan

Metric decompositions and the discrete isoperimetry

Abstract Intelligence is a kind, necessary in all stages and levels of system’s design and development This paper describes some of the local solutions, used in the Industrial Information Management systems, developed by the Academy of Sciences, Armenia, for the AimElectra JSC. Working with the process and production planning problems it supposed a distributed information system integrating technological, financial, supply chain and manufacturing process data types. Although the general level modeling principles are well known by the Enterprise Reference Architectures, there are a number of low-level problems, important for the whole system design and implementation. The paper considers the one of these layers - the work with object-oriented dictionaries. Proved, that the metric decompositions by the discrete isoperimetry property provide the automation for search, correcting and identification.

The splitting technique in monotone recognition

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. Hansels 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 Hansels technique for identification of monotone Boolean functions on all appearing binary cubes, and Alekseevs 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.