Showing papers on "Completeness (order theory) published in 1978"

On the completeness of query languages for relational data bases

Abstract: In this paper, we have studied the problem of completeness of relational query languages. We have etablished a criterion for completeness. A query language was proved to be complete. Since this language is the one used as a standard for completeness this results gives strong theoretical basis to Codd's definition of completeness.

Connectivity as an alternative to boundary integral equations: Construction of bases

Abstract: In previous papers Herrera developed a theory of connectivity that is applicable to the problem of connecting solutions defined in different regions, which occurs when solving partial differential equations and many problems of mechanics. In this paper we explain how complete connectivity conditions can be used to replace boundary integral equations in many situations. We show that completeness is satisfied not only in steady-state problems such as potential, reduced wave equation and static and quasi-static elasticity, but also in time-dependent problems such as heat and wave equations and dynamical elasticity. A method to obtain bases of connectivity conditions, which are independent of the regions considered, is also presented.

The Plurality of Science

Abstract: What I have to say falls under four headings: What is unity of science, unity and reductionism, the search for certainty, and the search for completeness.

Consistent and complete proof rules for the total correctness of parallel programs

Abstract: We describe a formal theory of the total correctness of parallel programs, including such heretofore theoretically incomplete properties as safety from deadlock and starvation. We present a consistent and complete set of proof rules for the total correctness of parallel programs expressed in nondeterministic form. The proof of consistency and completeness is novel in that we show that the weakest preconditions for each correctness criterion are actually fixed-points (least or greatest) of continuous functions over the complete lattice of total predicates. We have obtained proof rule schemata which can universally be applied to least or greatest fixed points of continuous functions. Therefore, our proof rules are a priori consistent and complete once it is shown that certain weakest preconditions are extremum fixed-points. The relationship between true parallelism and nondeterminism is also discussed.

Completeness of a set of modes connected with the electromagnetic field of a homogeneous sphere embedded in an infinite medium

Abstract: The mode decomposition of the electromagnetic field connected with a sphere is considered The sphere is embedded in an infinite medium The continuity requirements of the field across the surface of the sphere lead to a certain set of so called natural modes, which can be calculated explicitly if the radial part of the electric field strength inside the sphere equals zero The completeness of the radial parts of these modes, which is a set of spherical Bessel functions, is sometimes erroneously deduced from Sturm-Liouville theory This theory, however, cannot be used to show the completeness because the continuity conditions of the field lead to a boundary value problem with a boundary condition which explicitly depends on the eigenvalue The completeness of this set of functions, which is necessary to solve an initial value problem, will be shown

Some New Types of Logical Completeness

Abstract: In this paper, we consider the problem of determining if a given set of simple combinational functions, called logic primitives, can be used to realize any arbitrarily complex combinational function. The complex combinational function is realized by suitably interconnecting the primitives, and in most cases several copies of the primitives. Such a set of primitives is said to be complete in some sense. Two important types of logical completeness that have been previously studied are: 1) strong completeness where the circuit inputs are the uncomplemented variables x1,x2,···,xn, and 2) weak completeness where the circuit inputs are 0,1,x1,x2,···,xn. In this paper, we discuss two new types of logical completeness: strong c-completeness with inputs x1, x1, x2, x2,···,xn, xn and weak c-completeness with inputs 1, 0, x1, x1, x2, x2,···, xn, xn, and we derive necessary and sufficient conditions for a set of primitives to be strong c-complete or weak c-complete. We also discuss the relations between the above four types of completeness. Finally, we consider two more types, complement completeness and dual completeness, which may have applications to some recent technologies.

An extended owner-coupled set data model and predicate calculus for database management

Abstract: A data model is presented, based on the extension of the concept of a DBTG owner-coupled set to permit static and dynamic sets and a new kind of set referred to as a virtual set. The notion of connection fields is introduced, and it is shown how connection fields may be used to construct derived information bearing set names, and hence permit the specification of (dynamic) sets which are not predeclared in a schema. Virtual sets are shown to reflect the functional dependencies which can exist within a file. A technique which permits the data model to be fully described diagrammatically by extended Bachman diagrams is described. A predicate calculus for manipulation of this data model is presented. Expressions written in this calculus are compared with corresponding expressions in a relational predicate calculus, DSL ALPHA. An argument for the relational completeness of the language is given.

Design rules for producing logically complete two-process interactions and communications protocols

Abstract: This paper addresses the problem of protocol failures that are caused by logically incompletely specified designs. A design is logically complete if it specifies all occurrable event (message) receptions under normal operating conditions. A more stringent requirement is that of dual completeness. A design is dually complete if it neither contains unspecified event receptions nor unspecified event transmissions. Rules for creating dually-complete designs are established and a design methodology based on these rules is proposed. The problem of designing interactions that involve interrupt-masked computations is also treated.

Symmetries and Groups

Abstract: Let us now consider more formally the question of groups and symmetries. Mathematically a group is defined by a set of axioms, and for the sake of completeness these axioms are stated here.

Completeness problems for switching circuits constructed from delayed gates

Abstract: The capability of the synthesis of finite deterministic automata build up from delayed gates over a finite alphabet d is studied by reduce that problem to the problem of building circuits realising functions of several variables ranging over d and with values in d. Some characterizations for the completeness (strong, full and uniform completeness) of a set of delayed gates are given, and also for precomplete classes of a set of uniformly delayed gates.

Another Look at Scattering Theory

Abstract: We present a new approach to existence and completeness of wave operators. We do not use the subspace of absolute continuity, but rather the orthogonal complement of the eigenvectors. This is more natural from the physical point of view. We give sufficient conditions for existence and completeness of the wave operators. These results are both simpler and stronger than those obtained previously.

On formal specifications and completeness: reply to Farshid Nourani

Abstract: Nourani cites several results that derive from Godel's basic theorem o n the incompleteness of all formal systems that exceed a certain very minima l degree of complexity. The well-known results about first-order logic do appl y when first-order theories are used to specify abstract data types(1) ; however , it is not clear why this poses a problem with using first-order theories fo r that purpose .

The Complex Number System

Abstract: We denote the set of all real numbers by ℝ. It is assumed that each reader is acquainted with the real number system and all its properties. In particular we assume a knowledge of the ordering of ℝ, the definitions and properties of the supremum and infimum (sup and inf), and the completeness of ℝ (every non-empty set in ℝ which is bounded above has a supremum). It is also assumed that every reader is familiar with sequential convergence in ℝ and with infinite series. Finally, no one should undertake a study of Complex Variables unless he has a thorough grounding in functions of one real variable. Although it has been traditional to study functions of several real variables before studying analytic function theory, this is not an essential prerequisite for this book. There will not be any occasion when the deep results of this area are needed.