We show that the duality of a pair of monotone disjunctive normal forms of size n can be tested in n oŽlog n.

In this paper we focus on two powerful techniques to obtain compact clause normal forms: Renaming of formulae and reened Skolem-ization methods. We illustrate their eeect on various examples. By an exhaustive experiment of all rst-order TPTP problems, it shows that our clause normal form transformation yields fewer clauses and fewer literals than the methods known and used so far. This often al...

We axiomatize the congruence relation for binding bigraphs and prove that the generated theory is complete. In doing so, we define a normal form for binding bigraphs, and prove that it is unique up to certain isomorphisms. Our work builds on Milner’s axioms for pure bigraphs. We have extended the set of axioms with five new axioms concerned with binding, and we have altered some of Milner’s axi...

Previous work has shown that circuit representations can be exploited in QBF solvers to obtain useful performance improvements. In this paper we examine some additional techniques for exploiting a circuit representations. We discuss the techniques of propagating a dual set of values through the circuit, conversion from simple negation normal form to a more optimized circuit representation, and ...

We present a proof procedure that is complete for first-order logic, but which can also be used when searching for finite models. The procedure uses a normal form which is based on geometric formulas. For this reason we call the procedure geometric resolution. We expect that the procedure can be used as an efficient proof search procedure for firstorder logic. In addition, the procedure can be ...

Three universal approximation formulas given by so called disjunctive, conjunctive and additive normal forms are recalled. Properties and relations between all three formulas are studied. The quality of approximation is shown and the role of genetic algorithms in the field of fuzzy approximation is explained.

This paper introduces an incremental algorithm for learning a Boolean function from examples. The functions are constructed in the disjunctive normal form (DNF) or the conjunctive normal form (CNF) and emphasis is placed in inferring functions with as few clauses as possible. This incremental algorithm can be combined with any existing algorithm that infers a Boolean function from examples. In ...

ÐAs object-relational databases (ORDBs) become popular in the industry, it is important for database designers to produce database schemes with good properties in these new kinds of databases. One distinguishing feature of an ORDB is that its tables may not be in first normal form. Hence, ORDBs may contain nested relations along with other collection types. To help the design process of an ORDB...

In this paw=, a normal form for entity-relationship diagrams and the objectives for such a normal form are presented. A normal form entity-relationship diagram may consist of composite attributes, multivalued attributes, and special types of relationship sets such as existence dependent, identifier dependent, ISA, UNION, INTERSECT, and DECOMPOSE relationships. A comprehensive algorithm is given...

Parabolic Monge-Ampère equations are divided into contact inequivalent classes, for each of which a normal form is given. Two of these are new in the C category.