Existence and uniqueness of solution for synthesis problems of a class of gene regulatory networks

Recently, synthesis of gene regulatory networks having desired behavior has became of interest to many researchers and several studies have been done. We proposed synthesis methods of a class of gene regulatory networks based on expression patterns, in which desired behavior are given by expression pattern sequences. The theoretical investigation into the existence of solution of synthesis problems is a basic problem and is important. In this paper, we show the existence and the condition of uniqueness of solution of the synthesis problem based on expression patterns.