Analysing DNA microarray data using Boolean techniques

We address in this manuscript a problem arising in molecular biology, namely a problem of discovering dependencies among gene expression levels. The problem is formulated in mathematical terms as a search for a fully defined three valued function defined on three valued variables which is partially specified by the DNA microarray measurements. This formulation as well as our solution methods are strongly motivated by results in the area of logical analysis of data (LAD) and in the area of partially defined Boolean functions (pdBfs), in particular by procedures for finding fully defined extensions of pdBfs. On one hand we present several algorithms which (under some assumptions) construct the desired three valued functional extension of the input data, and on the other hand we derive several proofs showing that (under different assumptions) finding such an extension is NP‐hard.