Leontief Model Analysis with Fuzzy Parameters by Basic Matrixes Method

The basic matrixes method is suggested for the Leontief model analysis (LM) with some of its components indistinctly given. LM can be construed as a forecast task of product’s expenses-output on the basis of the known statistic information at indistinctly given several elements’ meanings of technological matrix, restriction vector and variables’ limits. Elements of technological matrix, right parts of restriction vector LM can occur as functions of some arguments. In this case the task’s dynamic analog occurs. LM essential complication lies in inclusion of variables restriction and criterion function in it.

Model Mining and Efficient Verification of Software Product Lines

Software product line modeling aims at capturing a set of software products in an economic yet meaningful way. We introduce a class of variability models that capture the sharing between the software artifacts forming the products of a software product line (SPL) in a hierarchical fashion, in terms of commonalities and orthogonalities. Such models are useful when analyzing and verifying all products of an SPL, since they provide a scheme for divide-and-conquer-style decomposition of the analysis or verification problem at hand. We define an abstract class of SPLs for which variability models can be constructed that are optimal w.r.t. the chosen representation of sharing. We show how the constructed models can be fed into a previously developed algorithmic technique for compositional verification of control-flow temporal safety properties, so that the properties to be verified are iteratively decomposed into simpler ones over orthogonal parts of the SPL, and are not re-verified over the shared parts. We provide tool support for our technique, and evaluate our tool on a small but realistic SPL of cash desks.