An experimental comparison of several simple inexpensive ways of doing pattern recognition when some data elements are missing (blank) is presented. Pattern recognition methods are usually designed to deal with perfect data, but in the real world data elements are often missing due to error, equipment failure, change of plans, etc. Six methods of dealing with blanks are tested on five data sets. Blanks were inserted at random locations into the data sets. A version of the K-nearest neighbor technique was used to classify the data and evaluate the six methods. Two methods were found to be consistently poor. Four methods were found to be generally good. Suggestions are given for choosing the best method for a particular application.

An improved procedure for resolution theorem proving, called Z-resolution, is described. The basic idea of Z-resolution is to “compile” some of the axioms in a deductive problem. This means to automatically transform the selected axioms into a computer program which carries out the inference rules indicated by the axioms. This is done automatically by another program called the specializer. The advantage of doing this is that the compiled axioms run faster, just as a compiled program runs faster than an interpreted program. A proof is given that the inference rule used in Z-resolution is complete, provided that the axioms “compiled” have certain properties.

Suppose a program P is written to accept a set of inputs I. If we are only interested in a nonempty subset $I^ * $ of I, we usually can simplify P to another program $P^ * $ such that $P^ * $ runs faster on $I^ * $ than P does. The problem of specialization is to find such $P^ * $. In this paper, the program P and the input $I^ * $ will be specified by axioms. Using these axioms, we can obtain $P^ * $ from P through theorem-proving techniques.

Many problems in artificial intelligence involve the searching of large trees of alternative possibilities—for example, game-playing and theorem-proving. The problem of efficiently searching large trees is discussed. A new method called “dynamic ordering” is described, and the older minimax and Alpha-Beta procedures are described for comparison purposes. Performance figures are given for six variations of the game of kalah. A quantity called “depth ratio” is derived which is a measure of the efficiency of a search procedure. A theoretical limit of efficiency is calculated and it is shown experimentally that the dynamic ordering procedure approaches that limit.