Business activities, in general, involve data processing (such as queries, extraction, manipulation, and restructuring of data, etc.) as well as conventional office work centered around preparation, distribution, and filing and retrieval of documents. Convinced that most of these activities can be expressed in terms of forms, we present in this paper a formal means for specification of forms processing. The underlying concept is that business functions can be decomposed into meaningfuliy connected form processes where each process either produces or modifies a form. Powerful constructs are provided so that most of the common data processing activities can be expressed in a very high level, concise, and yet compilable manner.

It is often possible to save storage space in a computer by storing only the differences among data items rather than the entire items. For example, suppose we have two records A and B. We should store all of A, then for B store a pointer to A and the differences between A and B. If A and B are similar, there will be few differences and storage space can be saved.

A clustering and data-reorganizing algorithm based on the concept of the shortest spanning path of a graph is given. This algorithm can be used to reorganize and/or cluster a large file of data.

A nearest neighbor classifier is one which assigns a pattern to the class of the nearest prototype. An algorithm is given to find prototypes for a nearest neighbor classifier. The idea is to start with every sample in a training set as a prototype, and then successively merge any two nearest prototypes of the same class so long as the recognition rate is not downgraded. The algorithm is very effective. For example, when it was applied to a training set of 514 cases of liver disease, only 34 prototypes were found necessary to achieve the same recognition rate as the one using the 514 samples of the training set as prototypes. Furthermore, the number of prototypes in the algorithm need not be specified beforehand.

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.

A piecewise linear function is represented in terms of a set of linear functions through the use of the maximum and minimum functions. A procedure for finding piecewise linear discriminant functions for pattern recognition is described. The procedure iteratively uses the accelerated relaxation method to find every linear function in a piecewise linear function. The procedure was implemented by a Fortran program. Experimental results with the program showed that the procedure is promising for obtaining piecewise linear discriminant functions.

A relaxation method mapping high-dimensional sample points to low-dimensional sample points is discussed. This method tries to preserve the local interdistance of sample points. Some special heuristics have been introduced to handle the difficulty arising from a large amount of data. Experimental results with handwritten character data and Iris data show that the method runs fast, converges rapidly, and requires a small amount of memory space.

Paramodulation can be used in conjunction with resolution for proving theoreIm in first-order logic with equality.Unit, input, and linear refutations using paramodulation and resolution are defined for theories with equality.It is proved that (a) if a set S of clauses has an input refutation, then S together with its unit factors and functionally reflexive axioms has a unit refutation; and (b) if C is a clause in an E-unsatisfiable set S of clauses including {x = x} and the functionally reflexive axioms and if (S -{C} ) is E-satisfiable, then S has a linear refutation with top clause C. ("E-unsatisfiable" is called "R-unsatisfiable" by some authors.)The refutation completeness theorem proved by Wos and Robinson for paramodulation with set of support is a corollary of our result (b).Our result (b) provides a link between heuristk programs and theorem-proving programs for first-order theories with equality. KEY WORDS AND PHRASES: theorem-proving,

A resolution in which one of the two parent clauses is a unit clause is called a unit resolution, whereas a resolution in which one of the two parent clauses is an original input clause is called an input resolution. A unit (input) proof is a deduction of the empty clause □ such that every resolution in the deduction is a unit (input) resolution. It is proved in the paper that a set S of clauses containing its unit factors has a unit proof if and only if S has an input proof. A LISP program implementing unit resolution is described and results of experiments are given.

This paper describes an algorithm which will generate all the prime implicants of a Boolean function. The algorithm is different from those previously given in the literature, and in many cases it is more efficient. It is proved that the algorithm will find all the prime implicants. The algorithm may possibly generate some nonprime implicants. However, using frequency orderings on literals, the experiments with the algorithm show that it usually generates very few ( possibly none) nonprime implicants. Furthermore, the algorithm may be used to find the minimal sums of a Boolean function. The algorithm is implemented by a computer program in the LISP language.