There are syntactically identifiable situations in which reduction does not occur in chain format linear deduction systems, i.e. situations in which linear-input subdeductions are performed. Three methods of detecting these situations are described in this paper. The first method (Horn subset analysis) focuses on Horn input chains while the second (LISS analysis) and third (LISL analysis) are s...

Some of the most successful algorithms for satisfiability, such as Walksat, are based on random walks. Similarly, local search algorithms for solving constraint optimization problems benefit significantly from randomization. However, well-known algorithms such as stochastic search or simulated annealing perform a less directed random walk than used in satisfiability. By making a closer analogy ...

closed families of sets. Poonen showed that if a finite union-closed family of sets S contains three of the 3−sets in some 4−set, then one of the elements of that 4−set is contained in at least half the members of the family S. This condition intrigued us, and we began to investigate collections of 3−sets for which it fails. The alternative statement that no 4−set contain more than two 3−sets i...

J. Chemom A new technique for representative subset selection is presented. The advocated method selects unambiguously the most important objects among the calibration set and uses this subset for themodel development without significant deterioration in the predictive ability. Themethod is called boundary subset selection and it is an inherent part of the Simple Interval Calculation (SIC) appr...

The usual data mining setting uses the full amount of data to derive patterns for different purposes. Taking cues from machine learning techniques, we explore ways to divide the data into subsets, mine patterns on them and use post-processing techniques for acquiring the result set. Using the patterns as features for a classification task to evaluate their quality, we compare the different subs...

This paper proposes a new method for combining forecasts based on complete subset regressions. For a given set of potential predictor variables we combine forecasts from all possible linear regression models that keep the number of predictors fixed. We explore how the choice of model complexity, as measured by the number of included predictor variables, can be used to trade off the bias and var...

The equivalence class subset algorithm is a powerful tool for solving a wide variety of constraint satisfaction problems and is based on the use of a decision function which has a very high but not perfect accuracy. Perfect accuracy is not required in the decision function as even a suboptimal solution contains valuable information that can be used to help find an optimal solution. In the harde...