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...

A number is normal in base b if every sequence of k symbols in the letters 0, 1, . . . , b− 1 occurs in the base-b expansion of the given number with the expected frequency b−k. From an informal point of view, we can think of numbers normal in base 2 as those produced by flipping a fair coin, recording 1 for heads and 0 for tails. Normal numbers are those which are normal in every base. In this...

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...

Several acoustic experiments show a surprising degree of stability in wave fronts propagating over multi-megameter ranges through the ocean's sound channel despite the presence of random-like, sound-speed fluctuations. Previous works have pointed out the existence of chaos in simplified ray models incorporating structure inspired by the true ocean environment. A "predictability horizon" has bee...

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.

The modular group plays an important role in many branches of mathematics. We show that the membership problem for the modular group is decidable in polynomial time. To this end, we develop a new syllable-based version of the known subgroup-graph approach. The new approach can be used to prove additional results. We demonstrate this by using it to prove that the membership problem for a free gr...

Herbrand and Skolemization theorems are obtained for a broad family of first-order substructural logics. These logics typically lack equivalent prenex forms, a deduction theorem, and reductions of semantic consequence to satisfiability. The Herbrand and Skolemization theorems therefore take various forms, applying either to the left or right of the consequence relation, and to restricted classe...

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 ...