The paper presents an algorithm for producing the logic conditions that result in the effects of a cause-effect graph belonging to a given software. These conditions yield the test cases of the software. The algorithm applies a three-valued Boolean algebra, and is based on the successive justification of logic values in a combinational network, where the primary inputs are the causes, and the primary outputs are the effects. The computations are performed by traversing a decision tree, where backtracking is required if a decision leads to a logic contradiction. The main advantage of the algorithm is that it reduces the number of decisions to a great extent by using don't care values in the process. The calculation principle is comparatively simple. It is based only on successive line-value justification, and it yields an opportunity to be realized by an efficient computer program. The logic model introduced in the paper is completely general, in that it is applicable to any kind of cause-effect graphs, without any constraint. © 2013 IEEE.