This paper describes learning in a compiler for algorithms solving classes of the logic minimization problem MINSAT, where the underlying propositional formula is in conjunctive normal form (CNF) and where costs are associated with the True/False values of the variables. Each class consists of all instances that may be derived from a given propositional formula and costs for True/False values by fixing or deleting variables, and by deleting clauses. The learning step begins once the compiler has constructed a solution algorithm for a given class. The step applies that algorithm to comparatively few instances of the class, analyses the performance of the algorithm on these instances, and modifies the underlying propositional formula, with the goal that the algorithm will perform much better on all instances of the class.

This paper describes a method for learning logic relationships that correctly classify a given data set. The method derives from given logic data certain minimum cost satisfiability problems, solves these problems, and deduces from the solutions the desired logic relationships. Uses of the method include data mining, learning logic in expert systems, and identification of critical characteristics for recognition systems. Computational tests have proved that the method is fast and effective.

In data mining, two types of errors may occur when records are classified into two categories A and B: misclassifying an item in A as one of B and conversely misclassifying an item in B as one of A. Tight control over these two errors is needed in many practical situations since, for example, an error of one type may have far more serious consequences than one of the other type. Most previous work on two-class classifiers does not allow for such control. We describe a general approach that supports tight error control for two-class classification and that can utilize any two-class classification method as part of the decision mechanism. The main idea is to construct from the given training data a family of classifiers and then, using the training data once more, to estimate two distributions of certain vote totals. The error control is achieved via the two estimated distributions. The approach has been tested using several well-known classification problems. In each case, the two estimated distributions were very close to those obtained from verification data. Accordingly, good error control can be achieved.

Abstract Computation of globally optimal flows in nonlinear gain networks is generally quite difficult. This paper identifies classes of these networks for which optimal solutions are easily obtained.

Abstract A graph‐theoretic characterization of unimodular matrices arising from flow problems with additional constraints is developed. The resulting necessary and sufficient conditions are utilized to determine the class of unimodular matrices of multicommodity transportation problems.

Abstract A simple and efficient procedure is presented which scales a network with gains to an equivalent one with positive or unit gains, provided certain necessary and sufficient conditions are satisfied.