MANBIS is a C++ mathematical software package for tackling the problem of computing the roots of a function when the number of roots is very large (of the order of hundreds or thousands). This problem has attracted increasing attention in recent years because of the broad variety of applications in various fields of science and technology. MANBIS applies the bisection method to obtain an approximate root according to a predetermined accuracy. Thus, the only computable information required is the algebraic signs of the considered function, which is the smallest amount of information (one bit of information) necessary for the purpose needed, and not any additional information. MANBIS is able to compute very efficiently a user-given percentage of roots and draws its strength from the fact that the roots are expected to be many. Furthermore, MANBIS is capable of estimating without any additional function computational cost the total number of roots within the user-given interval. Our approach can also be efficiently applied in cases where the distribution of the roots is not known. This article is accompanied by another article where the user manual, some implementation details, and some examples are included.

The application of single input change (SIC) pairs of test patterns is very efficient for sequential, i.e. stuck-open and delay fault testing. In this paper a novel implementation for the application of SIC pairs is presented and a formal proof of its completeness is provided. The presented generator is optimal in time, in the sense that it generates the n-bit SIC pairs in time n × 2n, i.e. equal to the theoretical minimum. Comparisons with the schemes that have been proposed in the open literature that generate SIC pairs in optimal time, reveal that the proposed scheme requires less hardware overhead.

We study the complexity of telling whether a set of bit-vectors represents the set of all satisfying truth assignments of a Boolean expression of a certain type. We show that the problem is coNP-complete when the expression is required to be in conjunctive normal form with three literals per clause (3CNF). We also prove a dichotomy theorem analogous to the classical one by Schaefer, stating that, unless P=NP, the problem can be solved in polynomial time if and only if the clauses allowed are all Horn, or all anti-Horn, or all 2CNF, or all equivalent to equations modulo two.